# Does an object accelerate under uniform circular motion?

This is part of a series on common misconceptions.

Is this true or false?An object performing uniform circular motion does not accelerate.

**Why some people say it's true:** In uniform circular motion, the speed remains constant.

**Why some people say it's false:** In uniform circular motion, the direction of motion keeps changing.

The statement is \( \color{red}{\textbf{false}}\).

Explanation:First, let's understand about the uniform circular motion. In uniform circular motion, a particle moves in a circular path with constant speed. As the speed of motion is constant, a confusion comes in that the acceleration is zero.

To clarify the confusion, let's look at the definition of acceleration. The acceleration is defined as the time rate of change of velocity. Therefore, whenever velocity changes, acceleration is present. The faster the velocity changes, the larger is the acceleration. Velocity is a vector quantity, so it can be changed by changing either the speed or the direction of motion.

In the case of uniform circular motion, the speed remains the same and the direction changes continuously. Therefore, there has to be an acceleration. The acceleration in the case of uniform circular motion always points toward the center of circular motion and is called as the centripetal acceleration. This centripetal acceleration is related with the angular velocity \(\omega \), radius \(R\), and the speed of motion \(v\) as \[{a_{\text{centripetal}}} = {\omega ^2}R = \frac{{{v^2}}}{R}.\]

Rebuttal: In the case of uniform circular motion, what is the angle between velocity and acceleration?

Reply: If the speed remains constant, then the component of acceleration which is parallel to the velocity is zero. This component is called as tangential acceleration. The direction changes due to the centripetal acceleration which is radially inward. Thus, the net acceleration in the case of uniform circular motion is perpendicular to the velocity.

Rebuttal: In the case of uniform circular motion, can the magnitude of acceleration be written as equal to the rate of change of speed?

Reply: No, the rate of change of speed is entirely different from the rate of change of velocity. Acceleration is defined as the rate of change of velocity.

A particle is moving on a circular track with constant non-zero speed. Which of the following options is/are correct?

(a) The acceleration of the particle is zero.

(b) The rate of change of speed equals the magnitude of the rate of change of velocity.

(c) Instantaneous speed equals the magnitude of instantaneous velocity.

(d) The angle between velocity and acceleration has to be \(90^\circ \).

**See Also**

**Cite as:**Does an object accelerate under uniform circular motion?.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/is-uniform-circular-motion-a-uniform-motion/