Problem

The centripetal force is the net force that tends to the center of the circle whenever there is uniform circular motion. The basic equation is

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Circular motion-0.png

Part 1: Express the speed in terms of the radius of the circle , and the period of one revolution . Then use the expression of velocity to express the centripetal force in terms of the period.

Part 2: The frequency is defined as the reciprocal of the period . Express the centripetal force in terms of frequency.

Solution

Part 1

The speed in uniform circular motion is the distance divided by the period. Since the distance is the circumference of the circle with radius ,

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Then

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Part 2

Since and

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