Solution:
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 \(N = \frac{\theta}{2\pi} = \frac{36\pi}{2\pi} = 18\).
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:
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