Question

Why is the motion of a body with a constant speed around a circular path said to be accelerated?

Answer 1

Hint: Motion in a circular path with a constant speed is called uniform circular motion. It is very important to understand the difference between a scalar and a vector quantity. For example speed is a scalar quantity and velocity is a vector quantity. A body in acceleration means there is a change in velocity with time. As vector quantity can be said to be changing even if only the direction is being changed, keeping the magnitude constant.

Complete step by step answer:
Speed is a scalar quantity and velocity is a vector quantity. If the speed is constant, it doesn’t imply that the acceleration is zero but if the velocity is constant, it always implies that acceleration is zero or motion is non-accelerated. Let’s consider the following diagram for more clarity.

In the above figure, we can see that a particle when rotates in a circle, at each and every point of path, its direction changes which is shown by arrows and is always tangential to the circle at each point. Hence the direction is changing continuously and that also means that velocity is changing at every point. Thus we can say that the motion is accelerated.
The acceleration associated with this type of motion, called uniform circular motion is called centripetal acceleration and is given by $a_C = \omega R^2$, where R is the radius of circle and ‘$\omega$’ is the constant angular speed of the particle undergoing motion. This acceleration is directed radially inwards.

Note:
We can see that the magnitude of this acceleration is constant with time. One should always analyze the quantities with their directions and magnitude separately. For example the magnitude of centripetal acceleration is $\omega R^2$ but its direction is radially inwards (along the string). The direction of acceleration is also changing at every point.