Question 4: Why is the acceleration of a body moving uniformly in a circle directed toward the center?

ANSWER

Since the body is moving with uniform speed, its tangential acceleration is zero. However, due to its circular motion it experiences a change in its radial or centripetal acceleration every moment.
This is because of the centripetal force acting continuously on the body and is directed toward the center of the circle. This can be understood by using a diagram of a body moving in a circle as shown.
Let the body is at a point ‘A’ on the circle at a particular instant of time. Suppose its velocity is represented by a vector at this point. Now after some time it moves to point ‘B’ on the circle and the corresponding velocity is. The change in velocity can be vectorally found.

Δ=–

By making θ small, we see that Δ becomes perpendicular to  and. But perpendicular to and are the radii of the circle at that points. Therefore,  the acceleration is always directed toward the center of the circle.

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