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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.fig2c5p11
Let the body is at a point ‘A’ on the circle at a particular instant of time. Suppose its velocity is represented by a vectorvaca at this point. Now after some time it moves to point ‘B’ on the circle and the corresponding velocity isvecb. The change in velocity can be vectorally found.

Δvecv=vecbvaca

By making θ small, we see that Δvecv becomes perpendicular tovaca  andvecb. But perpendicular tovaca and vecbare the radii of the circle at that points. Therefore,  the acceleration is always directed toward the center of the circle.

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