In this segment, we shall try to understand the difference between centripetal acceleration vs acceleration and various types of accelerations.
The notable difference between centripetal acceleration vs acceleration is that acceleration is the rate at which velocity and direction change with time. Whereas, centripetal acceleration acts on a body moving in a circular path that pulls the object towards the center.
|The acceleration acts on a body that is in a circular motion and tends to pull the body towards the centre.||The acceleration that acts on a body when it is in linear motion.|
|It is the rate of change of tangential velocity.||It is the rate of change of linear velocity.|
|It applies to an object having a specific radius.||It applies to the whole rigid body.|
|It causes a change in the direction of velocity.||It causes the speed to increase or decrease.|
|Formula – ac=V2/r||Formula – aL=Δv/Δt|
|S. I. Unit – m / s2||S. I. Unit – m / s2|
Centripetal Acceleration vs. Angular Acceleration
Centripetal acceleration and angular acceleration seem much like each other as both are observed when an object is following a circular path, but they are two very different phenomena.
The significant difference between centripetal acceleration and angular acceleration is that centripetal acceleration is the acceleration that functions on an object when it is travelling in a circular path, and a centripetal force tends to pull the object inwards or towards the centre.
Whereas angular acceleration is the acceleration that acts on an object about its centre of rotation and on an object that has a fixed origin. It is like a corkscrew that has a fixed direction. Angular acceleration draws the object either inside or outside the circle.
Centripetal acceleration is given as:
|Where,ac = Centripetal Acceleration.|
|V = Velocity of the object.|
|r = Radius of the circle.|
Angular acceleration is symbolized by the Greek alphabet ‘α’, and its formula is given as:
α = Δω/Δt
This equation can also be given as:
α = Δω/Δt = (ω2-ω1)/(t2-t1)
|Where,||α = Angular Acceleration.|
|ω = Angular velocity of the object.|
|ω2 = Final Angular Velocity.|
|ω1 = Initial Angular Velocity.|
|t = Time.|
|t2 = Final Time.|
|t1 = Initial Time.|
The delta ( Δ ) sign just shows the change in the quantity.
The S. I. Unit for angular acceleration is: rad / s2.
Centripetal Acceleration vs. Centrifugal Acceleration
Centripetal acceleration is the result of centripetal force that acts on an object perpendicularly and directs the object towards the center, due to which the motion of the object changes and moves in a circle. The more the centripetal force, the lesser is the radius of the circle.
Centripetal force works with the help of gravity, friction, tension, etc. However, centrifugal force is actually referred to as fictitious or pseudo forces. It is not a force and is only used in exceptional cases. Centrifugal acceleration is a reactionary acceleration to centripetal acceleration. It can also be said that the centrifugal acceleration comes into the picture when there is a shortage of centripetal acceleration.
Centrifugal acceleration is opposite to centripetal acceleration. Centrifugal acceleration has a centrifugal force that directs the object away from the centre. The greater the speeds of the revolving object, the further it will move from the centre.
The object itself applies centrifugal force. The tendency of an object is always to move in a straight line, but the centripetal force does not allow the object to move in a straight line, and thus the centrifugal force tries to pull the object away from the centre to move in a straight line. (One should not confuse centrifugal force or acceleration as linear force or acceleration).
Read more on Centripetal Force Examples, Critical FAQs.
Centripetal Acceleration vs. Radial Acceleration
The angular acceleration is divided into two types radial and tangential. In this segment of centripetal acceleration vs acceleration, we will study the difference between centripetal acceleration and radial acceleration.
The radial acceleration is perpendicular to the direction of the object’s movement and points towards the center, which roots a change in the direction of the object. Radial acceleration is very much similar to centripetal acceleration, but it is the negative of centripetal acceleration. Thus, the formula for radial acceleration is given as:
ar = – ac = –V2/r
|Where,||ar = Radial Acceleration.|
|ac = Centripetal Acceleration.|
|V = Velocity of the object.|
|r = radius of the circle.|
The negative sign in the equation just represents the direction of motion. The S. I. Unit for radial acceleration is the same as the angular acceleration = rad / s2.
Occasionally, centripetal acceleration itself is referred to as radial acceleration.
Some examples of radial acceleration, more commonly referred to as centripetal acceleration, are:
- The orbital motion of moons around their planets with the help of gravitational force.
- The orbital motion of the planets around the sun with the assistance of gravitational force.
- The orbital motion of electrons around the nucleus with the assistance of electrostatic force.
- The turning of vehicles on a curved path causes a circular motion.
Centripetal Acceleration vs. Gravitational Acceleration
Gravitational acceleration is the pull that an object experiences when it comes under the influence of gravitational force. The strength of the pull is described as gravitational acceleration. The value of gravitational acceleration is different for different planets, natural satellites, or any other astronomical body.
By Newton’s second law: F = mg
|Where,F = Force m = Mass of the object g = Gravitational Acceleration|
|Where,||F = Force|
|m = Mass of the object|
|g = Gravitational Acceleration|
|G = Gravitational Constant|
|r = distance between the objects|
The S. I. Unit for gravitational acceleration is m / s2.
As mentioned above, centripetal acceleration acts on an astronomical object due to or with the help of gravitational force.
The notable difference between centripetal acceleration vs gravitational acceleration is direction. The direction of centripetal acceleration is invariably towards the center, whereas gravitational acceleration is always downwards.
Also, read about Is kinetic energy conserved in an inelastic collision.
Centripetal Acceleration vs. Linear Acceleration
In this segment of centripetal acceleration vs acceleration, we shall try to enhance our knowledge about the similarities and differences between centripetal acceleration and linear acceleration.
The rate of change of velocity is known as acceleration, but in linear acceleration, the object will not change its direction. It will move in a straight line. So, the significant difference itself is the direction of motion of the object.
In linear acceleration, the speed of the object might increase or decrease. Whereas, in centripetal acceleration, only the direction of velocity changes. The objects moving in a straight line are known to be having rectilinear motion.
There are three basic formulae for finding velocity in which acceleration is involved. With the help of these formulas themselves, one can find acceleration.
v = u + at
x = ut + (1/2) at2
v2 – u2 = 2ax
|Where,||v = Final Velocity of the object.|
|u = Initial Velocity of the object.|
|a = Acceleration of the object.|
|t = Time taken by the object.|
|x = Distance covered by the object.|
Linear acceleration –
The S. I. Unit for linear acceleration is m / s2.
The significant similarity between linear acceleration and centripetal acceleration is that both are vector quantities consisting of both direction and magnitude. Also, acceleration, in any case can be positive or negative depending on if it is increasing or decreasing.
Lateral Acceleration vs. Centripetal Acceleration
Lateral means ‘of’, ‘at’, ‘towards’, or ‘from’ the side. So, the acceleration that is to the side is known as the lateral acceleration. It is the pull that is created outwards, and it is very much similar to centrifugal acceleration.
The lateral acceleration is experienced chiefly when a vehicle is in motion, especially when the vehicle is taking a turn or following a curved path. The lateral acceleration works on the opposite side of the motion of the car.
As shown in the picture below, the direction of lateral acceleration is always opposite to the movement of the car. Therefore, if the car is taking a left turn, the lateral acceleration of that car will be facing in the opposite direction, i.e., the right direction.
And if the car is taking a right turn, its lateral acceleration will be in the left direction. But the crucial information to keep in mind is that these directions will be measured with respect to the direction of the car and not that of the road.
Lateral acceleration is given as: aL = V2/r
|Where,||aL = Lateral Acceleration.|
|v = Velocity of the object.|
|r = radius of the circle.|
Lateral acceleration is a bit complicated subject as it occurs in two dimensions instead of one. People sitting in the car generally experience this force when a car is taking a turn, especially when it is a sharp turn.
Centripetal Acceleration vs. Tangential Acceleration
Tangential acceleration is the acceleration that works at the tangent of a circle. Tangential acceleration and centripetal acceleration are perpendicular to each other. The tangential acceleration is an outcome of change in speed, whereas the centripetal acceleration is an outcome of change in direction.
The concept of tangential acceleration is a tricky concept as tangential acceleration follows a linear motion, but not on a straight or a linear path, it instead works on a circular or a curved path.
The formula for tangential acceleration can be given as:
aT = (radius of the circle) x (angular acceleration)
aT = rα
aT = r*dω/dt
|Where,||aT = Lateral Acceleration.|
|α = Angular Acceleration|
|r = Radius of the circle.|
|ω = Angular Velocity|
|t = Time.|
Hence, tangential acceleration is accountable for the change in the linear speed of an object but on a curved path.
If the speed of the object is persistent (there is no acceleration), then the value for tangential acceleration will be zero. The value of the tangential acceleration will be positive when the object’s speed increases. The value of the tangential acceleration will be negative when the object’s speed decreases.
The difference between centripetal acceleration vs tangential acceleration can be understood from the picture presented above. The centripetal acceleration will point towards the centre, and it will constantly be changing its direction. Therefore centripetal acceleration will never be zero, which will cause the tangential acceleration to occur.
The net acceleration can be found using the vector addition formulae as both are vector quantities.
To understand the addition of vectors, read Is force a Vector Quantity.