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The angular velocity of the second hand of a watch is:

1. $30\pi$
2. $2\pi$
3. $\pi$
4. $60\pi$

Correct answer: $30\pi$

Solution

The second hand completes one full revolution in 60 s, so its angular velocity is $\omega = \frac{2\pi}{60} = \frac{\pi}{30}$ rad/s. The options appear OCR-corrupted; the intended correct value corresponds to $\frac{\pi}{30}$ rad/s. Since the provided answer text is $30\pi$, the question likely contains an OCR error in the options.

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