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A rock on a string undergoes uniform circular motion at a constant radius and with period...

A rock on a string undergoes uniform circular motion at a constant radius and with period T (i.e., it makes one complete revolution around the circle in time T). As a result, the magnitude of the centripetal acceleration of the object is a c. Suppose now the motion is changed so that the period is T/2 but the radius is the same. What will be the new magnitude of the centripetal acceleration

ac/2

2ac

4ac
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Answer #1

Let the radius of the circle be r and the angular speed of the rock be . Then the magnitude of centripetal acceleration of the rock is given by,

If T is the time period, then

Therefore,

When the new time period T' = T/2, then the magnitude of new centripetal acceleration is,

So the new magnitude of the centripetal acceleration is 4.

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