Capturing fast-moving subjects with a camera can be a challenging task, but with the right lens and camera settings, you can freeze the action and create stunning images. In this comprehensive guide, we’ll dive deep into the technical aspects of lens selection and camera settings to help you master the art of photographing fast motion. … Read more
Types of relative motion can be of different frame of references too. There is no particular type for the relative motion but there exists relativity in motion between any two frames of references.
When we consider the object that is in motion it will acquire certain properties and these properties change when they encounter another object to be in motion too. The types of motion can be of great help to actually determine the types of relative motion.
Firstly we need to know what exactly the rectilinear motion is. The rectilinear motion is the motion of objects which travel in the same line of space.
When any two bodies are said to move in the same direction and in the co joints then are said to be in rectilinear motion. Also there exists a relative motion between these two bodies. For example when two cars move in the same direction in the same line then they have relative motion.
The motion between them differs in terms of velocity, speed, frequency and so on. They have relative motion that will be differing at different factors affecting them. It is also similar to the case where two people are moving in the same line of queue but have different speeds with which they move.
Next will be the frame of references that we need to consider here, when two bodies are travelling in the same line of space given. So when two points are on the reference we join them and get a triangle.
Rectilinear motion is when the objects move in a straight line without any deviation. And when two such bodies travel in the straight line we tend to calculate the relative motion between the objects in motion.
When the path of the motion of an object is in circles then the motion is said to be in circular motion.
When the object moves in such a manner then the motion of the path is described by the circumference of the circle. And it also describes the length of the circle which is nothing but the circumference of the circle.
Now let us make use of an example of motion which will easily explain this types of motion. We consider the satellite that circles the earth in its own circular path.
The satellite will create a circular motion as the path of direction form this we know that there is circular motion form a certain height form the earth. There are several other satellite too that will circle around the earth.
When other satellites come into contact with each other there seems to be a relative motion between the satellites. The speed of one satellite may vary from the other satellite and when the orbit around the earth one seems to be in stationary while the other seems to be in circular motion, and vice versa.
Another example is that, when you tie one end of string to a stone and the other end is whirled around then it automatically makes a circular motion. So when two such stones are made to whirl around there said to be in relative motion to each other.
We consider one plate of the fan while in its motion then it is said to undergo a circular motion. But when we consider the whole fan system then the system is said to be under the rotational motion.
Generally when the motion is said to be circular then it should move along the circumference but in this case it doesn’t. The whole fan system is considered as one single object and for an observer the motion of the fan seems to be stationary as all the plates of the fan move at great speed.
Consider a person lying on the floor while the fan is switched on so when we are stationary the fan also seems to be in stationary state. But the actual fact is that the speed of the fan is in such a way that it moves at great speed and we notice it to be not moving.
The axle is called the point of rotation about which all the plates are connected to one single rotor which drives the plates of the fan into motion and this motion is relative to the observer.
The axial motion is regarded to be the motion in which the object rotates in circular motion along with the axis of its rotation.
How is the type of relative motion comes under this section you might think. The answer is simple and can be explained using a real world experience. Let us consider the solar system for this purpose.
Now we all know that the planets in the solar system rotate and revolve in a certain direction at certain speed. So we shall see the earth as the best example for this. When earth rotates on its axis, it’s relative to the motion which it revolves around the earth.
From the earth if we see other planets they seem to move in the opposite direction or they seem to be in motion, but we do not realise that we too are in constant circular motion.
It is called the relative motion in general. The motion of earth and the other planets are in relative to each other. So we take other satellites to be in motion and they seem to appear in stationary state from viewed from other satellites.
For example say a satellite is launched form India is revolving around but the satellite form Chine too revolving around the earth. The two satellites are said to be on relative motion to each other. The motion between the planets and satellites can be one of the best examples for the types of relative motion.
Relative Motion In One And One Dimensional Motion
Generally when we consider a motion of any object we say that they are acting under from different frames of reference.
But there are certain times where the motion occurs in one or two dimensional. Generally a projectile motion is considered to be the one dimensional motion because it moves in one single direction.
But when a football is kicked or thrown from one end to another there will be a relative motion between the player and the ball and the player on the receiving end. We call this a tow dimensional motion where the relative motion comes into act.
Generally when the motion of any object that occurs in two different direction at the same time. So there will certainly be a relative motion between the objects.
In a one dimensional motion we consider a projectile motion and also a falling object, Here only the object thrown or falling is in relative to the person on the other. Therefore we consider this motion to be one of the types of relative motion.
Relative motion is a fundamental concept in physics that describes the motion of an object with respect to another object or frame of reference. It allows us to understand how objects move and interact in relation to each other. In this section, we will explore the definition of relative motion, discuss its importance, and provide examples of its application in various fields.
Definition of Relative Motion
Relative motion refers to the movement of an object in relation to another object or frame of reference. It involves analyzing the position, velocity, displacement, speed, and direction of an object from the perspective of an observer or reference frame. By considering the motion of one object relative to another, we can gain insights into the dynamics and behavior of the system as a whole.
Importance of Understanding Relative Motion
Understanding relative motion is crucial in many areas of science and engineering. It allows us to analyze and predict the behavior of objects in motion, enabling us to design and optimize various systems. Here are a few reasons why understanding relative motion is important:
Physics: In physics, relative motion is essential for studying the laws of motion and understanding the principles of mechanics. It helps us describe the motion of objects in different reference frames and analyze the forces acting upon them.
Transportation: Relative motion plays a vital role in transportation systems. For example, when driving a car, understanding the relative motion of other vehicles is crucial for maintaining a safe distance and avoiding collisions. Similarly, in aviation and maritime industries, pilots and captains need to consider the relative motion of other aircraft or vessels to navigate safely.
Sports: Relative motion is also relevant in sports. Athletes often need to anticipate the movement of their opponents and adjust their own motion accordingly. For example, a soccer player needs to consider the relative motion of the ball and other players to make accurate passes or shots.
Astronomy: Relative motion is crucial in astronomy to understand the movement of celestial bodies. By considering the relative motion of planets, stars, and galaxies, astronomers can predict celestial events, such as eclipses and planetary alignments.
Examples of Relative Motion in Various Fields
Relative motion can be observed in various fields and everyday scenarios. Here are a few examples:
Car overtaking another car: When a car overtakes another car on a highway, the relative motion between the two vehicles is evident. From the perspective of the overtaking car, the other car appears to move backward, while from the perspective of the other car, the overtaking car appears to move forward.
Train passing a stationary observer: When a train passes a stationary observer, the relative motion between the train and the observer is apparent. The observer sees the train moving past them, while the train passengers perceive the observer as stationary.
Boat crossing a river: When a boat crosses a river, the relative motion between the boat and the river is significant. The boat’s motion is a combination of its own velocity and the velocity of the river’s current. This relative motion affects the boat’s path and speed.
Person walking on a moving treadmill: When a person walks on a moving treadmill, the relative motion between the person and the treadmill is evident. From the perspective of an observer standing still, the person on the treadmill appears to be moving forward, even though their actual displacement is zero.
In conclusion, understanding relative motion is essential for comprehending the dynamics of objects in motion. It allows us to analyze the motion of objects from different perspectives and reference frames, enabling us to make accurate predictions and design efficient systems. Whether in physics, transportation, sports, or astronomy, relative motion plays a crucial role in our understanding of the world around us.
Examples of Relative Motion in Everyday Life
Relative motion refers to the motion of an object with respect to another object or observer. It is a concept commonly used in physics to describe how objects move in relation to each other. Let’s explore some examples of relative motion in everyday life.
Imagine standing on a train platform as a train approaches. From your perspective, the train appears to be moving. However, if you were on the train, you would perceive the platform as moving in the opposite direction. This is an example of relative motion, where the motion of the train is relative to the motion of the platform.
Consider a scenario where you are sitting on a moving train and looking out the window. As the train moves, you notice a person standing on the platform. From your perspective, the person appears to be moving backward. However, from the perspective of an observer on the platform, the person is stationary. This difference in perception is due to the relative motion between you, the train passenger, and the observer on the platform.
Two Cars in Motion
When two cars are moving in the same direction, their relative motion is determined by the difference in their velocities. If one car is traveling at a higher speed than the other, it will appear to be moving away from the slower car. On the other hand, if the two cars are moving in opposite directions, their relative motion will be the sum of their velocities. This concept of relative motion helps us understand how objects move in relation to each other.
Imagine you are in a park, and you see a child running across a field. From your perspective, the child’s motion is relative to your position. If you were to move to a different location in the park, the child’s motion would appear different. This example illustrates how an observer’s position affects their perception of relative motion.
Bird and the Airplane
Have you ever noticed a bird flying alongside an airplane? From the bird‘s perspective, it is flying relative to the air around it. However, from the perspective of an observer on the ground, the bird and the airplane appear to be moving together. This is an example of relative motion, where the motion of the bird is relative to the motion of the airplane.
When you observe a river flowing, you might notice that the water appears to be moving. However, if you were to stand on a boat in the middle of the river, the water would seem stationary. This is because the boat is moving with the water, and its motion is relative to the river’s motion. The concept of relative motion helps us understand how objects move in different reference frames.
Car and Treadmill
Imagine a scenario where a car is placed on a treadmill. As the treadmill moves backward, the car‘s wheels spin to keep up with the motion. From an observer’s perspective, it may seem like the car is moving, but in reality, it is stationary. This example demonstrates how relative motion can be deceptive and influenced by the frame of reference.
Motion of a Table
Consider a table placed on a moving train. From the perspective of a passenger on the train, the table appears to be stationary. However, from an observer standing outside the train, the table is moving along with the train. This example highlights how relative motion can vary depending on the observer’s perspective.
In conclusion, relative motion is a fundamental concept in physics that helps us understand how objects move in relation to each other. These everyday examples of relative motion demonstrate how an object’s motion can be perceived differently depending on the observer’s perspective and frame of reference. By studying relative motion, we can gain a deeper understanding of the dynamics of objects in motion.
Examples of Relative Motion in the Solar System
The concept of relative motion is crucial in understanding the dynamics of objects in the solar system. By observing the motion of celestial bodies from different reference frames, we can gain valuable insights into their behavior. In this section, we will explore some fascinating examples of relative motion in the solar system.
Earth and Sun
One of the most fundamental examples of relative motion in the solar system is the relationship between the Earth and the Sun. From our perspective on Earth, it appears as though the Sun rises in the east and sets in the west. However, this apparent motion is actually a result of the Earth’s rotation on its axis.
In reality, the Sun remains relatively stationary while the Earth rotates. This rotation gives us the illusion of the Sun’s motion across the sky. Additionally, the Earth orbits around the Sun, completing one revolution every 365.25 days. This orbital motion is responsible for the changing seasons we experience throughout the year.
Motion of Planets
The motion of planets in the solar system provides another captivating example of relative motion. When observing the planets from Earth, we can see them move across the night sky against the backdrop of stars. This apparent motion is a result of both the Earth‘s and the planets‘ orbital motions.
From our perspective on Earth, some planets appear to move in a retrograde motion, where they briefly reverse their direction of motion against the backdrop of stars. This retrograde motion occurs when the Earth overtakes and passes by a slower-moving outer planet in its orbit around the Sun.
The relative motion of planets can also be observed during planetary conjunctions. A conjunction happens when two or more planets appear close to each other in the sky. These celestial events provide a stunning visual display and allow astronomers to study the interactions between different celestial bodies.
In summary, the examples of relative motion in the solar system, such as the Earth’s rotation and orbit around the Sun, as well as the motion of planets, offer a fascinating glimpse into the dynamic nature of our cosmic neighborhood. By understanding and studying these relative motions, we can deepen our knowledge of the solar system and the laws of physics that govern it. Conclusion
In conclusion, understanding the concept of relative motion is crucial in various fields, including physics, engineering, and everyday life. Relative motion refers to the movement of an object in relation to another object or frame of reference. By considering the relative motion of objects, we can analyze and predict their behavior accurately. Whether it’s calculating the velocity of a moving car from the perspective of a stationary observer or determining the trajectory of a projectile in relation to the Earth’s rotation, relative motion plays a significant role. By grasping the principles of relative motion, we can better comprehend the world around us and make informed decisions based on this understanding. So, the next time you observe objects in motion, remember to consider their relative motion to gain a deeper insight into their behavior and interactions.
Frequently Asked Questions
1. What is the definition of relative motion?
Relative motion refers to the motion of an object in relation to another object or reference frame. It is the motion observed from the perspective of an observer in a particular reference frame.
2. Can you provide an example of relative motion in physics?
Certainly! An example of relative motion in physics is when two cars are moving in the same direction on a highway. To an observer in one car, the other car appears to be moving slower. However, to an observer on the side of the road, both cars appear to be moving at different speeds.
3. How is relative motion explained with an example?
Let’s consider a person walking on a moving train. From the perspective of the person on the train, their motion is relative to the train. However, from the perspective of an observer standing outside the train, the person’s motion is a combination of their walking motion and the motion of the train.
4. What are some examples of relative movement?
Examples of relative movement include a cyclist passing a pedestrian, a boat moving against the current of a river, or a person walking on a moving escalator. In each case, the motion of one object is observed in relation to another object or reference frame.
5. Can you provide examples of relative velocity?
Certainly! Examples of relative velocity include a car overtaking another car on a highway, a person walking on a moving sidewalk, or a bird flying against the wind. In each case, the velocity of one object is observed relative to another object or reference frame.
6. What is the frame of reference in relation to motion?
A frame of reference is a coordinate system used to describe the position, motion, and properties of objects. It provides a fixed point of reference from which measurements and observations can be made.
7. How does an observer’s perspective affect the perception of motion?
An observer’s perspective determines how they perceive the motion of objects. Depending on their position and reference frame, the same motion can appear different to different observers. This is the basis of relative motion.
8. What is the difference between velocity and speed in relative motion?
Velocity is a vector quantity that includes both magnitude and direction, while speed is a scalar quantity that only represents magnitude. In relative motion, both velocity and speed can vary depending on the observer’s perspective.
9. How is relative displacement calculated in relative motion?
Relative displacement is calculated by subtracting the initial position of an object from its final position, taking into account the observer’s perspective. It represents the change in position relative to a reference frame.
10. What role does direction play in relative motion?
Direction is an essential component of relative motion as it determines the orientation of an object’s motion relative to a reference frame. It helps describe the path or trajectory followed by an object in relation to another object or observer.
circular motion is a fascinating concept that involves objects moving along a curved path. One of the key factors in circular motion is the normal force. In this blog post, we will explore the concept of normal force in circular motion, understand its role, and learn how to calculate it. We will also dive into practical examples and address frequently asked questions about normal force in circular motion.
What is Normal Force in Circular Motion?
Definition and Explanation of Normal Force
Before we delve into normal force in circular motion, let’s first understand what normal force is. In physics, the normal force is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular to the surface and prevents the object from sinking into or passing through the surface.
In the context of circular motion, the normal force plays a crucial role in keeping an object moving along a curved path. It provides the necessary centripetal force to keep the object in circular motion and prevents it from flying off in a straight line.
The Role of Normal Force in Circular Motion
In circular motion, the normal force acts as the centripetal force. It is directed towards the center of the circular path and always perpendicular to the surface of contact. Without the normal force, an object in circular motion would lose its curved path and continue moving in a straight line tangent to the circle.
Differences between Normal Force and Other Forces
It’s important to differentiate normal force from other forces that come into play during circular motion. The normal force is distinct from the gravitational force, which acts vertically downwards due to the object’s weight. The normal force acts perpendicular to the surface and is responsible for the circular motion of the object.
How to Calculate Normal Force in Circular Motion
Understanding the Formula for Normal Force in Circular Motion
To calculate the normal force in circular motion, we need to consider the components of forces acting on the object. In most cases, we have the gravitational force (weight) and a centripetal force acting towards the center of the circular path.
The formula for calculating the normal force in circular motion is:
where:
– N represents the normal force,
– m is the mass of the object,
– g is the acceleration due to gravity,
– v is the velocity of the object, and
– r is the radius of the circular path.
Step-by-Step Guide on How to Calculate Normal Force
Let’s walk through a step-by-step guide to calculating the normal force in circular motion:
Determine the mass of the object (m).
Determine the radius of the circular path (r).
Determine the velocity of the object (v).
Calculate the gravitational force (mg).
Calculate the centripetal force (( frac{{mv^2}}{r} )).
Add the gravitational force and the centripetal force to obtain the normal force (N).
Common Mistakes to Avoid When Calculating Normal Force
When calculating the normal force, it’s important to avoid common mistakes that can lead to incorrect results. Some common mistakes include:
Forgetting to include the gravitational force in the calculation.
Using the wrong formula for calculating the centripetal force.
Using the wrong units for mass, velocity, or radius.
To ensure accuracy, double-check the formulas and units before performing the calculations.
Practical Examples of Finding Normal Force in Circular Motion
Now, let’s apply our knowledge of calculating the normal force in circular motion to some practical examples.
Example of Finding Normal Force in Uniform Circular Motion
Suppose we have a car moving in a uniform circular motion on a flat surface. The car has a mass of 1000 kg and is moving with a velocity of 20 m/s. The radius of the circular path is 10 meters. To find the normal force, we can use the formula:
Substituting the given values into the formula, we have:
Simplifying the equation, we find:
Therefore, the normal force acting on the car is 49800 N.
Example of Finding Normal Force in Vertical Circular Motion
Let’s consider a scenario where an object is moving in a vertical circular motion. The object has a mass of 2 kg and is moving with a velocity of 5 m/s. The radius of the circular path is 3 meters. To find the normal force, we can again use the formula:
Substituting the given values into the formula, we have:
Simplifying the equation, we find:
Therefore, the normal force acting on the object is 36.27 N.
How to Interpret the Results of Your Calculations
After calculating the normal force, it’s important to interpret the results correctly. The normal force represents the force exerted by the surface to support the weight of the object and provide the necessary centripetal force for circular motion.
If the calculated normal force is greater than the weight of the object (mg), it means there is an additional force acting towards the center. This indicates that the object is experiencing an upward force, thereby maintaining circular motion.
On the other hand, if the calculated normal force is less than the weight of the object (mg), it means the surface is unable to provide enough force to sustain circular motion. The object might lose contact with the surface and deviate from its circular path.
The concept of normal force in circular motion intersects with the idea of finding tangential acceleration by considering the forces acting on an object in circular motion. In circular motion, there is a centripetal force acting towards the center of the circle, which is provided by the normal force. The normal force is perpendicular to the surface the object is moving on and counteracts the gravitational force. By understanding the normal force, we can calculate the net force and determine the resulting tangential acceleration using the principles explained in “Finding Tangential Acceleration: A Complete Guide.” This guide provides a comprehensive explanation of the various factors and equations involved in finding tangential acceleration in circular motion.
Frequently Asked Questions about Normal Force in Circular Motion
Image by Ilevanat – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 3.0.
Why is Normal Force Important in Circular Motion?
The normal force is essential in circular motion as it provides the necessary centripetal force to keep the object moving along a curved path. Without the normal force, an object in circular motion would veer off in a straight line tangent to the circle. It ensures that the object remains on the circular path and does not lose contact with the surface.
How Does the Normal Force Change in Different Types of Circular Motion?
The normal force can vary in different types of circular motion. In scenarios where the object is moving on a flat surface, the normal force remains constant unless additional forces are acting on the object. However, in situations involving inclined planes or vertical circular motion, the normal force may change due to the angle or orientation of the surface.
What Factors Can Affect the Normal Force in Circular Motion?
The normal force in circular motion can be influenced by various factors. These factors include the mass of the object, the velocity of the object, the radius of the circular path, and the angle or orientation of the surface. Changes in any of these factors can lead to variations in the normal force.
By understanding these factors and their impact on the normal force, we can better analyze and predict the behavior of objects in circular motion.
By now, you should have a solid understanding of how to find the normal force in circular motion. Remember to carefully consider the forces at play, utilize the appropriate formula, and follow a step-by-step approach to ensure accurate calculations. With practice, you’ll be able to tackle more complex scenarios and gain a deeper insight into the fascinating world of circular motion.
A body is acknowledged to be in motion if it changes its position with respect to its encompassing in a given time.
Periodic motion vs simple harmonic motion can be explained as, A body is said to be in periodic motion if it continuously Repeats its motion on a particular path in a certain period of time. While on the contrary,simple harmonic motion can be acknowledged as the simplest form of vibratory or oscillatory motion.
Periodic Motion
Periodic motion can be understood by motion which we observe on a daily basis. In periodic motion, it is not necessary that the displacement that occurred in the body is in the direction of the restoring force.
For instance, the earth completes its one rotation on its own axis in 1 day. The motion of the moon is also a periodic motion as we know that the moon completes one revolution around the earth in approx. 27 days.
Similarly, the motion of hands in our clock is also a periodic motion. These all motions keep on repeating themselves in a particular path and in a certain period of time.
Simple Harmonic Motion
Simple harmonic motion can be understood as the periodic motion oneself because simple harmonic motion is a type of oscillatory motion. Where a vibratory motion or oscillatory motion is assumed as a body, which is performing periodic motion and moves along the definite path back and forth about a definite position (fixed position), then the motion of the body is known as ‘vibratory motion’ or ‘oscillatory motion.’
periodic motion vs simple harmonic motion
vibratory or oscillatory motion
In the above-given figure, we can see that that the body is moving back and forth from the fixed position. Here the body oscillates from the fixed point O to the other side, covering maximum displacement to A, and then comes back to position fixed position O and then goes to another side A’ covering maximum displacement. From point A’ body comes forth to fixed point O again. this back and forth motion done by a body is said to complete ‘1 vibration’ or ‘1 oscillation’.
However, it is proved that each oscillatory motion is automatically a periodic motion, but each periodic motion is not a vibratory or oscillatory motion. For instance, the earth rotates on its own axis but does not move back and forth about a certain point along a path (this is an essential condition for an oscillatory motion that is not followed in the given case.).
Simple harmonic motion has a sine wave waveform of amplitude vs time.
time displacement curve of a body performing SHM
In the above-given figure, the time-displacement curve of a body oscillating back and forth about its fixed position is shown. The displacement y is measured from the fixed position, and the time t is measured from the point when the body passes through its fixed position. One oscillation is completed from point O to point A, and the time T taken for one oscillation is the periodic time of the body.
The maximum value of displacement y in the given figure will be a. this maximum displacement is known as amplitude. The total number of oscillations that a body performs in a time period of 1 second is known as frequency. The frequency (n)is the reciprocal of the time period.
When a body vibrates, its position and direction of motion vary with time. The phase of a vibrating body at any point of time shows the motion of the body at that point of time. At any point in time, two vibrating bodies are passing simultaneously through their equilibrium positions in the same direction, then at that instant, they are in the same phase, and if they are passing in opposite directions, then they are in opposite directions.
Irrespective of periodic motion, Simple harmonic motion needs certain conditions to be satisfied:-
For simple harmonic motion, the body should be in a straight line moving back and forth about a fixed position
The restoring force acting on the body should always be proportional to the displacement of the body from the point.
Restoring force is when a body takes the place of its stable position. Now a recurrent force acts upon it, which is directed towards the stable position. It is due to this force that acceleration is produced in the body, and it starts vibrating back and forth
This force is given by :
F= -kx
when restoring force is proportional to the dislocation of the body from the stable position, then the rate of change of velocity of the body is also proportional to the dislocation of the body, and it vibrates, performing the simple harmonic motion.
Where k is force constant and x is displacement and – sign indicates that the body is displaced in the opposite direction.
The force should always be directed towards the fixed point.
Simple harmonic motion can be explained through the following examples. A body attached to a spring in a horizontal plane produces vibrations which are simple harmonic in nature, oscillations by a simple pendulum, the motion of a body dropped in an imaginary tunnel across the earth, oscillations of a body floating in liquid, newton cradle, swings, oscillation of a body in the neck of an air chamber.
We can conclude the difference between periodic motion vs simple harmonic motion on the basis of restoring force that acts on the body performing oscillations which are supposed to be proportionate to the dislocation of the body, whereas periodic motion repeats itself continuously without any given conditions.
Frequently Asked Questions
Two conditions are given as follow:-
General vibration of a polyatomic molecule about its configuration is such a case. they have different natural frequencies and due to this its oscillation there is a superposition of SHM of a number of variable frequencies. this superposition is periodic but not SHM.
Revolution of the earth around sun is periodic but it is not a SHM.
Frequency and time period of a particle performing SHM are related as-
A simple pendulum is a particular form of the pendulum in which the length of the string is much larger compared to the mass of the suspended body. For the example of simple harmonic motion, we can take The motion of a simple pendulum. On striking the mass hanging from the string, it starts moving to and fro. In this condition, a restoring force arises to oppose the movement of the body.
In the figure above, we can see that the pendulum is moving from central point to either side and then passing through that it reaches the maximum point. The maximum distance between central point on both sides is its amplitude. This is an amplitude of motion example.
Swing
The swings in the children’s playground are another amplitude of motion example. When we apply force using the weight of our body, the swing starts moving forward and backward. Along with force generated by us, a restoring force also starts acting to restrict the motion of the swing. Now the maximum displacement that the swing makes in the forward or backward direction is inferred as its amplitude. Greater amplitude more will be the restoring force. The swing reaches higher when its amplitude is greater.
Musical instruments like violin, guitar, and sitar are taken as examples of simple harmonic motion. When we strike the string, they start making vibrations. These vibrations start generating sound waves. When these waves enter our ears, we hear music.
The strings of these instruments are displaced to the maximum distance, which is known to be the amplitude of motion. If we beat the strings with great intensity, it would result in a larger amplitude. Since the restoring force varies directly with the amplitude, it would increase too. But the other factors of motion balance out the effect.
Spring
A bob dangling from an upright spring is also an example of simple harmonic motion. When we hang a body, the spring stretches to some extent and then comes into constant upwards and downwards motion. A force comes into action to restrict the motion.
In the diagram above, the initial position of the spring is. When we attach a mass, it stretches to the point and comes into motion. The displacement is the amplitude of the moving spring. Whether it is a vertical or horizontal arrangement, the amplitude is found in the same way.
Bungee jumping is an adventurous activity in which a person tied to a string jumps off the cliff. Bungee jumping has two steps, one the free fall. And the other after free in which the strings extend till full length and pull the person up. And hence the string comes into simple harmonic motion.
The force acts on the string in an upward direction that opposes its motion in a downwards direction. The force here concerns Hooke’s law. The gravitational force acts in a downward direction. Hence the person oscillates up and down. Now the extent to which the person is pulled is the amplitude of the string or cord.
Eardrums
Without simple harmonic motion, hearing is not possible. A vibrating body produces sound waves. These waves reach the eardrum and start vibrating it. The motion of the eardrum is the simple harmonic motion.
It is also the amplitude of motion examples. The motion of the eardrum can be shown in the wave diagram. The peak distance is the amplitude of the motion. Louder sound leads to high amplitude, and softer or low sound leads to low amplitude.
Cradle
This is one of the basic examples, the physics behind it is very simple and easy to understand. A cradle is a baby’s bed, also known as a rocker, as it keeps rocking to make them fall asleep. To bring the cradle in motion, it has to be struck and start moving backward and forwards. Now the height till which the cradle rises is known as its amplitude.
Torsion Pendulum
The torsion pendulum is the one whose weight rotates in the opposite direction alternatively. Usually, it has a disc attached to the string, which twists, and the motion comes into action. It is an example of angular simple harmonic motion.
Since it is an angular simple harmonic motion, therefore, its amplitude is defined as the maximum angular displacement of the mass from the central position. For the motion to be angular simple harmonic, the amplitude should be kept small. If the circumstance reverses, then the motion would no more be simple harmonic.
Bouncing Ball
Abouncing ball is just a simple toy. When you strike it hard on the ground, it starts bouncing up and down. The amplitude of this ball is the maximum height it attains while in motion. Hence, it is also the amplitude of motion examples.
Frequently Asked Question (FAQs)
What are the types of motion?
In physics, there are different types of motion based on various factors.
The motions are categorized into six varied types. They are translation movement, rotational, oscillation, and uniform circular motion, and periodic motion. Further, we can also classify them into vibrational and simple harmonic motion.
Explain simple harmonic motion.
Simple harmonic motion is a particular type of periodic motion.
The simple harmonic motion is the one in which an object makes to and fro movement. During the motion, a force emerges that tries to oppose the movement.The movement of the pendulum and spring is an instance of simple harmonic motion.
What is the amplitude of a motion?
The amplitude is one of the defining terms of the motion.
Amplitude is the absolute measure of the displacement of the body or object from the mean position.It can be negative and only suggests that displacement is done in the opposite path.Amplitude is denoted by the symbol A, and its units are meters.
Explain the amplitude of motion examples.
The spring of strings of musical instruments and bungee jumping are all amplitude of motion examples.
When we hang a mass on the spring, it stretches to some extent and then comes into motion. The maximum displacement of the spring gives the value of its amplitude.
What is the amplitude of a pendulum?
A Pendulum is a simple instrument with a bob of the mass hanging from a string.
The pendulum moves to and fro, making oscillations. See the figure above, and you can see that the amplitude of the pendulum is the distance to which it extends to both sides.
Simple harmonic motion is a form of periodic motion in which an object or particle moves about its central position. Let us know what is amplitude of motion.
In SHM, when a body moves about a fixed point, it covers displacement on either side of the point. This maximum displacement covered by a particle or object is termed the amplitude of motion. There is a possibility of it being negative, which only shows the displacement in the opposite direction.
We all have seen or know that it starts vibrating for a few seconds on striking the guitar string. It first moves from its equilibrium position to one side and then goes to the other side from passing through to the equilibrium position. Now, this whole to and fro motion of the string is the periodic motion.
Here one more thing arises when the string starts vibrating, a restoring force emerges, which acts directly proportional to the particle’s displacement. Hence this is a simple example of simple harmonic motion.
In this example, the displacement of the string on either side of the central position is its amplitude. Let us understand it in a simple method. When we march past, our hands swing front and back. Now the extent to which you lift your hand will be its amplitude.
In this figure, we can see that the particle is making equal maximum displacement on either side. Therefore the distance XY is the amplitude of the motion. The symbol to symbolize amplitude is A, and since it is a measure of displacement, its standard unit is meter (m). There can be another unit as well, like centimeters.
How to calculate the amplitude of motion
We have understood what is amplitude of motion now; the next question that arises is how to calculate the amplitude of motion. The simple harmonic motion is a sinusoidal wave function; therefore, the SHM equation can be represented as a function of sine or cosine.
x = A sin (ωt + ϕ) or x = A cos (ωt + ϕ)
Here,
x is the displacement of the wave
A is the amplitude of motion
ω is the angular frequency
t is the period
ϕ is the phase angle
From the above equation, we can calculate the amplitude of the motion.
Suppose we are given the SHM equation as x = 2sin(4t). Now, comparing the equation with sinusoidal wave equation x = A sin (ωt + ϕ), we get amplitude as 2 metres.
What is amplitude of motion
For the given diagram, we can easily calculate the amplitude. From the figure, the amplitude is 5 m.
Frequently Asked Question (FAQs)
What is simple harmonic motion?
In physics, motion can be varied, like simple harmonic, wave, and circular motion.
The simple harmonic motion is the to and fro movement of a particle or object. In this motion, the restoring force acts indirectly proportional to the amplitude. Example: musical instruments, bungee jumping etc.
Is SHM the same as a periodic motion?
Periodic motion is the one in which a body repeats its motion in regular intervals.
Simple harmonic motion is a particular case of periodic motion in which, on movement, a restoring force emerges, which increases or decreases with the amplitude of the motion.
What is amplitude of motion?
To define a simple harmonic motion, we use some basic physics concepts. One of them is amplitude.
Amplitude is the maximum displacement that a body or particles complete about its central point. Suppose a bouncing ball reaches a maximum height of 50 cm, then the amplitude of the ball becomes 50 cm.
Give an example of the amplitude of motion.
The amplitude of motion is the maximum displacement of a moving body.
In the above figure, we can see that the pendulum displaces on either side till point A and B. Therefore, the distance OA and OB become the amplitude of the moving pendulum.
How to calculate the amplitude of motion?
The simple harmonic motion is a sinusoidal wave function. Its equation can be represented as s sine or cosine function.
The SHM equation is represented as:
x = A sin (ωt + ϕ) or x = A cos (ωt + ϕ)
Here,
x is the displacement of the wave
A is the amplitude of motion
ω is the angular frequency
t is the period
ϕ is the phase angle
The equation is used to calculate the amplitude of the motion.
On what factors does amplitude depend?
Amplitude depends only on the energy of the moving body.
Amplitude is directly proportional to the square root if dissipated energy. It further does not depend on any other factor of SHM like frequency or time period.
How does amplitude affect the motion?
The restoring force that emerges is directly varied to the amplitude of motion.
The rise in amplitude leads to an increase in the force, which further increases the acceleration. The amplitude does not have any effect on the frequency and angular frequency. Therefore amplitude does not affect the motion.
What is the symbol and unit of the amplitude of motion?
The amplitude of a moving particle is the distance between the central and extreme points.
The amplitude of the motion is denoted by the symbol A since it is the measure of displacement, therefore its unit meters.It gives the idea about the extent the body can move and gain the highest position.
When a particle moves in a straight line to and fro about its equilibrium position, then the particle’s motion is called ‘simple harmonic motion.let discuss simple harmonic motion examples.
When a point mass has a weightless, inextensible, and perfectly flexible string that is suspended from rigid support, then such an arrangement is known as a simple pendulum. If we slightly displace the point mass to one side and release it. Then in such circumstances, the simple pendulum starts swinging, to and fro from its mean position. This swinging of a simple pendulum in a straight line from its mean position is an example of simple harmonic motion.
a simple pendulum
Oscillation of guitar strings
A musical instrument like guitar strings is an example of simple harmonic motion. When we twang a guitar string, The string starts moving to and fro. First, strings of guitar move forward and then move in the opposite direction. This motion causes vibration. These vibration created by guitar strings creates sound waves that human ears hear as music
Car Suspension
A car suspension system contains springs, as the springs have elasticity property whenever there is any bump the spring compresses which results in rising of cars wheels without actual rising the car body similarly when springs expand it causes the wheel to drop without the actual dropping of car body this causes to and fro motion which is Simple harmonic motion. Although this type of motion is damping which means it reduces over a period of time. This simple harmonic motion reduces the shock which passengers receive when a car goes across a bump.
Hearing
It is due to Simple harmonic motion that living organism has the ability to hear. When the vibrating molecules come upon our eardrums, it causes our eardrums to wobble. These vibrations caused in our eardrums are passed to organisms’ brains. In due course, these details are transmitted to the organism’s brain through auditory nerves, the brain then translates these vibrations into apprehensible sounds.
Bungee Jumping
Simple harmonic motion examples can also be seen in our sports, for example, bungee jumping. In an adventurous sport like bungee jumping, a long recoiling cable is tied up to the person’s legs. Then person performs bungee jumping jumps from a particular platform situated at height.
When the person jumps off the cliff, due to the recoiling cable, he is pulled back and again moves down due to gravity; this keeps ongoing. As a repetitive to and fro motion can be seen in bungee jumping, it is an example of simple harmonic motion.
Swing
Swings can easily be seen in amusement parks, gardens, schools, etc. The motion shown in swings is known as simple harmonic motion because while swinging, the child sitting on it experiences the force acting upon it, which is directly proportional to its displacement and directed towards the equilibrium position. This causes the back and forth, repetitive motion of the swing, causing simple harmonic motion.
Newton’s Cradle
Simple harmonic motion can be seen in Newton’s cradle. This is an apparatus that shows the principle of conservation of momentum and the principle of conservation of energy.
Newtons cradle consists of 5 metal balls suspended by string so that the movement of spheres is in one place. All balls are placed so that all orbs are at rest and all balls are in contact with the adjacent ball. In newtons cradle, when the endmost sphere is taken from rest and pulled and released, the sphere starts swinging like a pendulum, and the released sphere hits the adjacent ball.
When the adjoining sphere comes in contact with the released sphere, the energy and momentum from the released ball are transmitted through the three balls at rest to the final ball on the other endmost sphere. The transfer of energy and momentum causes the ball to be in motion with the same speed as the first ball. If more than one sphere is pulled up and released, then the same number of balls, as much released, will be set in motion from the end of the resting spheres. Here we can see oscillation of the balls ( to and fro). They are showing simple harmonic motion.
newton’s cradle
Motion of a body in a hole drilled through the center of the earth
Imagine if we have a tunnel through the earth’s center and a body having some mass released inside it. Then due to gravitational attraction, force, which acts upon the body, moves towards the earth’s center. Here the body will never fall to another side of the hole of the earth due to variation in the gravitation constant ‘g, which is maximum at the surface and zero at the center of the earth.
When the body falls toward the center of the earth, it only reaches the center, then again gravitational pull is exerted on it due to which moves back again in the opposite direction. This process keeps ongoing. This periodic motion of the body inside the earth hole is a simple harmonic motion. However, this is a theoretical example of Simple harmonic motion.
a ball performing SHM
Mass loaded on springs
when a mass is suspended from the lower end of the springs, then due to its weight, the length of the spring is increased. Due to the elasticity of springs, it exerts a restoring force, due to which its moves again in the opposite direction. When we pull, the mass is suspended slightly downward and released. Then it oscillates up and down along with loaded mass, which is an example of Simple harmonic motion.
Oscillation of block in liquid
Oscillation of block in liquid is also an example of simple harmonic motion. When the block is pushed down a little into the liquid and left, it begins to oscillate up and down in the liquid showing simple harmonic motion.
Oscillation of block in liquid
Torsion pendulum
The torsion pendulum is an example of angular simple harmonic motion. A torsion pendulum consists of a disc that is suspended by a thin wire. When it is twisted and released, it moves back and forth direction executing simple harmonic motion. A torsion pendulum rotates in place of the swing. Such types of pendulums are used in a mechanical wristwatch.
torsional pendulum showcasing SHM
Oscillation of a ball in an air chamber
A ball in an air chamber having a long neck also shows simple harmonic motion. Suppose we consider a ball in the neck of an air chamber having air pressure in it. The air pressure in the container is atmospheric. If we slightly push down the ball in the neck of the air chamber, the ball will start oscillating up and down, showing simple harmonic motion.
oscillation of a ball in an air chamber showing SHM
Angular equations of motion are fundamental concepts in physics that describe the rotational motion of a body over time. These equations are crucial for understanding and analyzing the behavior of various systems, from simple rotating objects to complex machinery and celestial bodies. In this comprehensive guide, we will delve into the intricacies of angular equations of motion, providing a detailed exploration of the key principles, formulas, and practical applications.
Understanding Angular Displacement, Velocity, and Acceleration
The angular position of a body is measured in radians, which is the ratio of the arc length to the radius of curvature on a circular path. The angular displacement is the change in angular position and is also measured in radians. The linear displacement of a point on a rotating segment can be calculated using the equation d = rθ, where d is the linear displacement, r is the radius, and θ is the angular displacement expressed in radians.
Angular velocity is the first derivative of angular displacement with respect to time, and it is measured in radians per second (rad/s). Angular acceleration, on the other hand, is the second derivative of angular displacement with respect to time, and it is measured in radians per second squared (rad/s^2).
Rotational Kinematics Equations
The fundamental equations that describe the relationships between angular displacement, velocity, and acceleration are known as the rotational kinematics equations. These equations are analogous to the linear kinematics equations, but they are applied to rotational motion.
The rotational kinematics equations are:
θ = θ₀ + ω₀t + (1/2)αt²
Where θ is the final angular displacement, θ₀ is the initial angular displacement, ω₀ is the initial angular velocity, α is the angular acceleration, and t is the time.
ω = ω₀ + αt
Where ω is the final angular velocity, ω₀ is the initial angular velocity, α is the angular acceleration, and t is the time.
ω² = ω₀² + 2α(θ - θ₀)
Where ω is the final angular velocity, ω₀ is the initial angular velocity, α is the angular acceleration, θ is the final angular displacement, and θ₀ is the initial angular displacement.
These equations can be used to solve a variety of problems involving rotational motion, such as the one presented in the initial example.
Measuring Angular Motion
Angular motion can be measured using various instruments and techniques, such as gyroscopes, accelerometers, and optical encoders. Gyroscopes, for example, can be used to measure angular velocity by detecting the Coriolis effect, which is the apparent deflection of a moving object due to the rotation of the reference frame.
Accelerometers, on the other hand, can be used to measure angular acceleration by detecting the changes in the acceleration of a rotating body. Optical encoders, which are commonly used in robotics and industrial applications, can measure angular displacement by detecting the rotation of a marked wheel or disk.
One example of a sensor that can be used to measure angular motion is the enDAQ sensor. This sensor can be used to measure angular velocity and acceleration by formatting the sensor, acquiring the data, numerically differentiating the quaternion array to find the angular velocity, and calculating the angular velocity and acceleration in the reference basis.
Applications of Angular Equations of Motion
Angular equations of motion have a wide range of applications in various fields, including:
Robotics and Automation: Angular equations are used to control the motion of robotic arms, wheels, and other rotating components.
Aerospace Engineering: Angular equations are used to analyze the motion of spacecraft, satellites, and other rotating bodies in space.
Mechanical Engineering: Angular equations are used to design and analyze the performance of rotating machinery, such as gears, pulleys, and flywheels.
Sports and Recreation: Angular equations are used to analyze the motion of objects in sports, such as the rotation of a basketball or the swing of a golf club.
Astronomy and Astrophysics: Angular equations are used to study the motion of celestial bodies, such as planets, stars, and galaxies.
Numerical Examples and Problems
To further illustrate the application of angular equations of motion, let’s consider a few numerical examples and problems:
Example 1: A flywheel with a radius of 0.5 m is initially at rest. It is then accelerated at a constant rate of 2 rad/s^2 for 10 seconds. Calculate the angular displacement, angular velocity, and linear displacement of a point on the flywheel’s rim.
Solution:
– Initial angular velocity, ω₀ = 0 rad/s
– Angular acceleration, α = 2 rad/s^2
– Time, t = 10 s
Using the rotational kinematics equations:
– Angular displacement, θ = θ₀ + ω₀t + (1/2)αt² = 0 + 0 × 10 + (1/2) × 2 × 10² = 100 rad
– Angular velocity, ω = ω₀ + αt = 0 + 2 × 10 = 20 rad/s
– Linear displacement, d = rθ = 0.5 × 100 = 50 m
Problem: A wheel with a radius of 0.3 m is rotating at an initial angular velocity of 10 rad/s. If the wheel is subjected to a constant angular acceleration of 2 rad/s^2 for 5 seconds, calculate the final angular displacement, angular velocity, and linear displacement of a point on the wheel’s rim.
Solution:
– Initial angular velocity, ω₀ = 10 rad/s
– Angular acceleration, α = 2 rad/s^2
– Time, t = 5 s
Using the rotational kinematics equations:
– Angular displacement, θ = θ₀ + ω₀t + (1/2)αt² = 0 + 10 × 5 + (1/2) × 2 × 5² = 87.5 rad
– Angular velocity, ω = ω₀ + αt = 10 + 2 × 5 = 20 rad/s
– Linear displacement, d = rθ = 0.3 × 87.5 = 26.25 m
These examples demonstrate how to apply the rotational kinematics equations to solve problems involving angular motion, including the calculation of angular displacement, angular velocity, and linear displacement.
Conclusion
Angular equations of motion are essential tools for understanding and analyzing the rotational motion of various systems. By mastering the concepts of angular displacement, velocity, and acceleration, as well as the rotational kinematics equations, you can solve a wide range of problems in fields such as robotics, aerospace engineering, mechanical engineering, and astrophysics.
This comprehensive guide has provided a detailed exploration of the key principles and applications of angular equations of motion, equipping you with the knowledge and skills to tackle complex problems involving rotational motion. Remember to continue exploring the resources and references provided to deepen your understanding and stay up-to-date with the latest advancements in this fascinating field of study.
References
Basile Graf. “Quaternions and Dynamics.” arXiv preprint arXiv:0811.2889 (2008).
D.M. Henderson. “Euler Angles, Quaternions, and Transformation Matrices.” NASA Technical Report (1977).
Angular frequency (ω) is a fundamental concept in the study of simple harmonic motion (SHM), a type of periodic motion that is characterized by a restoring force that is proportional to the displacement from the equilibrium position. This guide will provide a detailed exploration of angular frequency in the context of SHM, covering its definition, mathematical formulation, and practical applications.
Understanding Angular Frequency in SHM
Angular frequency, denoted by the symbol ω, is a measure of the rate of change of the angle of oscillation in a simple harmonic motion. It is defined as the change in angle per unit time and is expressed in radians per second (rad/s). The angular frequency is a crucial parameter in the study of SHM, as it determines the frequency and period of the oscillation.
The relationship between angular frequency (ω) and the period (T) of a simple harmonic oscillator is given by the formula:
ω = 2π/T
where T is the time it takes for the oscillator to complete one full cycle of motion.
Calculating Angular Frequency in SHM
To calculate the angular frequency of a simple harmonic oscillator, you can use the following steps:
Determine the period (T) of the oscillation, which is the time it takes for the oscillator to complete one full cycle.
Substitute the period (T) into the formula: ω = 2π/T
Simplify the calculation to obtain the angular frequency (ω) in radians per second (rad/s).
For example, if the period of a simple harmonic oscillator is 2 seconds, the angular frequency would be:
ω = 2π/T
ω = 2π/2
ω = π rad/s
This means that the oscillator completes one cycle every 2 seconds and that the angle of oscillation changes by π radians every second.
Relationship between Angular Frequency and Frequency
In the context of wave motion, the angular frequency (ω) is related to the frequency (f) of the wave through the equation:
ω = 2πf
where f is the number of cycles completed per unit time, measured in hertz (Hz).
For example, if the frequency of a wave is 2 Hz, the angular frequency would be:
ω = 2πf
ω = 2π(2)
ω = 4π rad/s
This means that the wave completes 2 cycles every second and that the angle of oscillation changes by 4π radians every second.
Practical Applications of Angular Frequency in SHM
Angular frequency has numerous practical applications in the study of simple harmonic motion, including:
Pendulum Motion: The angular frequency of a pendulum is used to determine its period and frequency of oscillation, which is important in the design of clocks and other timekeeping devices.
Mass-Spring Systems: The angular frequency of a mass-spring system is used to analyze the motion of the system, such as the natural frequency of vibration and the response to external forces.
Electrical Circuits: In electrical circuits, the angular frequency is used to describe the rate of change of the voltage and current in alternating current (AC) circuits, which is crucial in the design and analysis of these circuits.
Wave Propagation: In the study of wave motion, the angular frequency is used to describe the rate of change of the phase of the wave, which is important in the analysis of wave interference, diffraction, and other wave phenomena.
Quantum Mechanics: In quantum mechanics, the angular frequency is used to describe the rate of change of the phase of the wave function, which is a fundamental concept in the study of the behavior of particles at the quantum level.
Numerical Examples and Problems
Example 1: A simple harmonic oscillator has a period of 3 seconds. Calculate the angular frequency of the oscillator.
Solution: ω = 2π/T
ω = 2π/3
ω = (2/3)π rad/s
Example 2: A wave has a frequency of 5 Hz. Calculate the angular frequency of the wave.
Solution: ω = 2πf
ω = 2π(5)
ω = 10π rad/s
Problem 1: A mass-spring system has a spring constant of 50 N/m and a mass of 2 kg. Calculate the angular frequency of the system.
Given:
– Spring constant, k = 50 N/m
– Mass, m = 2 kg
Problem 2: A pendulum has a length of 1 meter and is located on Earth, where the acceleration due to gravity is 9.8 m/s^2. Calculate the angular frequency of the pendulum.
Given:
– Length of the pendulum, l = 1 m
– Acceleration due to gravity, g = 9.8 m/s^2
These examples and problems demonstrate the application of angular frequency in the analysis of simple harmonic motion and wave propagation, highlighting the importance of this concept in various areas of physics and engineering.
Conclusion
Angular frequency is a fundamental concept in the study of simple harmonic motion and wave propagation. It is a measure of the rate of change of the angle of oscillation and is a crucial parameter in the analysis of various physical systems, from pendulums and mass-spring systems to electrical circuits and quantum mechanical phenomena. By understanding the mathematical formulation and practical applications of angular frequency, students and researchers can gain a deeper understanding of the underlying principles governing the behavior of these systems.
