Kinematics of Circular Motion

Practice Questions:

Question 11: moderate

The kinetic energy \((K)\) of particle moving along a circle of radius \(R\) depends upon the distance covered \(S\) and is given by \(K = aS\) where \(a\) is a constant. Then the centripetal force acting on the particle is:

1. \(\frac{aS}{R}\)

2. \(\frac{2(aS)^2}{R}\)

3. \(\frac{aS^2}{R}\)

4. \(\frac{2aS}{R}\)

View Answer

Kinetic energy is \(K = \frac{1}{2}mv^2 = aS\). Centripetal force is \(F_c = \frac{mv^2}{R}\) ( Since \(mv^2 = 2aS\), we get \(F_c = \frac{2aS}{R}\).

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Question 12: easy

A particle start revolving on a circular path with constant angular acceleration \(\frac{\pi}{2}\text{ rad/sec}^2\). Then find number of cycles it will complete in first 12 seconds:

1. \(12\text{ cycles}\)

2. \(18\text{ cycles}\)

3. \(36\text{ cycles}\)

4. \(72\text{ cycles}\)

View Answer

Angular displacement is \(\theta = \frac{1}{2}\alpha t^2 = \frac{1}{2} \left(\frac{\pi}{2}\right) (12)^2 = 36\pi\text{ rad}\). Number of cycles \(N = \frac{\theta}{2\pi} = \frac{36\pi}{2\pi} = 18\).

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