Can Centripetal Acceleration Be Zero: 7 Important Facts


Before knowing can centripetal acceleration be zero, we must understand the concept of centripetal acceleration. Here centripetal acceleration is the acceleration produced in any material when it travels along the circular path.

Can centripetal acceleration be zero can be said as follows; If centripetal acceleration is zero, then there will be no circular force that intends to make the particles travel along the circular path. It is necessary to understand the concept in detail because it helps us know about the different facts of zero centripetal acceleration.

The topic of discussion here is whether centripetal acceleration can be zero, which is understood clearly by reading down the facts below.

can centripetal acceleration be zero
Image: Centripetal acceleration

What do you mean by centripetal acceleration?

The centripetal acceleration of any object is defined as one of the important states of motion that a body undergoes. It always takes place on a circular path, and the acceleration acting on that particular body is always pointed towards the middle of the circular path.

The word centripetal always means towards the centre, and acceleration is a term that refers to the change in velocity of any material when it is the state of some motion in a certain path.

What is the formula of centripetal acceleration?

There is an existence of acceleration when a change occurs in the velocity of the moving body. If the body moves circularly, then there is centripetal acceleration, and it can be calculated using a specified formula that is mentioned below,

                                                            ac =  v2/r

Here,

ac indicates the centripetal acceleration acting on the object

v refers to the velocity that is acting on the moving object

r signifies the radius of the circular path on which the body moves

can view the centripetal acceleration formula in terms of newton’s second law of motion. We can also consider centripetal force, and by replacing a value with angular velocity ω, we can link it to the centripetal acceleration.

                                                              F = m * ω² * r 

A centripetal force is some action that leads to centripetal acceleration that is observed in satellite, swing and string cases.

When is centripetal acceleration zero?

In a circular motion, the velocity and direction the particle travels will change. Especially during tangential acceleration, the particle or the angular velocity will be uniform or constant, leading to zero tangential acceleration.

Let’s consider the case of uniform linear motion. The particle’s velocity will be constant since it moves on the straight path that automatically leads to zero acceleration, but in a circular motion, the case is different. The radial velocity will be non-zero, while the tangential velocity will be zero.

From this, we can interpret that the centripetal acceleration will be zero at this velocity.

 What do you mean by uniform circular motion?

When any object travels around the circular path with a constant speed(direction is not considered), that particle’s motion is defined as uniform circular motion. As the object passes along the circular path, the direction of its movement keeps on varying as it travels; its movement will be tangential towards the circular path.

The velocity vector of the body will be directed towards the tangent of the circular path, which is seen in the path of motion of the object.

Why is centripetal acceleration zero?

 The tangential part of centripetal acceleration will be zero since the angular velocity of the particle in that direction will have a constant value. Will direct the centripetal forces acting on the particle Fr towards the middle of the circular path.

If the particle moves with constant speed along the circular path, only at this point will the centripetal acceleration be non-zero.

Is centripetal acceleration always zero?

In a circular motion, the object travels in a path that is 90 degrees to the radial direction. Here if we take the dot product, then it will be zero. From this, we can observe that the work done by the centripetal force of the body during its motion will be zero.

 In this case, we can observe that when the centripetal force is zero, the centripetal acceleration will automatically become zero.

What happen when the centripetal acceleration is zero?

If the centripetal acceleration is zero, then even the centripetal force will be zero. Without these two factors acting on a particle, it can never move in a circular path.

Without centripetal acceleration and centripetal force acting on the particle, it will continue to move on the linear path. It will never diverge from that direction, and only this force can make the particle change the direction and make it undergo an inward .

Real-world examples of zero centripetal acceleration

We often find various examples of centripetal acceleration in our daily routine. It can be driving a vehicle around a circular path or an artificial satellite orbiting around the planet.

Some of the important real-world examples of zero centripetal acceleration are listed below,

  • Car changing its direction
  • Rotating a string
  • Roller Coaster
  • Playing

Car changing its direction

When a person whirls the ball attached to the string over-head, then centripetal acceleration acts on the ball that drives it towards the centre. Still, if there is zero centripetal acceleration, the ball moves in a linear direction. It is a real-world example of zero centripetal acceleration.

can centripetal acceleration be zero
Image Credit: Pixabay free images

Rotating a ball with a string

When an individual drives the car around the circular road, the car is pulled towards the mid-point through centripetal acceleration. Still, if there is zero centripetal acceleration, the car travels in a linear direction. It is one of the important real-life examples of zero centripetal acceleration.

Roller Coaster

Everyone usually enjoys the roller coaster ride; it is a fun play. But we should know that centripetal acceleration is the phenomenon that helps the roller coaster take sharp turns and helps it to stay on its track during its motion. If there were zero centripetal acceleration, then we would miss the experience of the twists and turns of roller coasters.

can centripetal acceleration be zero
Image Credit: Pixabay free images

Playing

While playing, if we continuously run around the circular path, then we feel some force that is drawing us towards the centre; this special centripetal force is due to centripetal acceleration that is taking place due to continuous change in direction and velocity; if there was zero centripetal acceleration, then it was not possible to take turns while running around the circle.

can centripetal acceleration be zero
Image Credit: Group of school children, Uncletomwood at English Wikipedia, CC BY-SA 3.0 via Wikimedia commons

These are some of the important real-world examples of zero centripetal acceleration.

Can centripetal acceleration be zero at the poles of the earth?

The centripetal acceleration will be weak or zero at the earth’s poles, and it will be more at the equator part of the earth.

The centripetal acceleration will be zero or weakest at the poles because the distance from the object to its axis of rotation will be less, leading to less centripetal force. Since centripetal force has centripetal acceleration, it will be zero.

Can we consider that any object moving in a circular motion has zero centripetal acceleration?

 If the motion is in the tangential direction of centripetal, then we can consider that the object moving in a circular path will have zero centripetal acceleration. The object will be in its accelerating motion when moving in a circular path, even when the velocity is constant.

The particle that moves on the circular will be accelerating, and the accelerating particles are considered objects that keep changing their velocity or direction. Any object that travels in a uniform circular motion will always possess constant velocity, even though it will be accelerating because of its constant change in the direction of motion.

Can acceleration be zero in case of uniform circular motion?

In any object travelling around the circular path, the centripetal acceleration will be zero only in the direction of tangential acceleration, and it happens due to the constant angular velocity of the object.

So, in a uniform circular motion, centripetal acceleration’s tangential direction will always be zero.

Can we say that the centripetal acceleration of any object ever be zero?

If we observe any material or body increasing or decreasing its speed during the motion, there is a non-zero tangential acceleration that acts in the path of motion. But if there is no variation in the velocity of the object moving on the circular path, then only at that point is centripetal acceleration, not zero.

Therefore, the tangential acceleration that acts on the path will be zero.

Conclusion

Therefore, we can summarize that any object moving in a uniform circular motion will possess tangential and centripetal acceleration. The tangential acceleration will be zero as the body’s angular velocity will be constant. In contrast, if the centripetal acceleration is zero, then there is no presence of circular motion.

Raghavi Acharya

I am Raghavi Acharya, I have completed my post-graduation in physics with a specialization in the field of condensed matter physics. Having a very good understanding in Latex, gnu-plot and octave. I have always considered Physics to be a captivating area of study and I enjoy exploring the various fields of this subject. In my free time, I engage myself in digital art. My articles are aimed towards delivering the concepts of physics in a very simplified manner to the readers. Let’s connect through - LinkedIn: https://www.linkedin.com/in/raghavi-c-s-260a801b1 EMAIL ID: raghavics6@gmail.com

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