Question

For a smoothly running analog clock, the angular velocity of its second hand in rad s\(^{-1}\) is:

• A. \(\frac{\pi}{1540}\)
• B. \(\frac{\pi}{720}\)
• C. \(\frac{\pi}{360}\)
• D. \(\frac{\pi}{12}\)
• E. \(\frac{\pi}{30}\)

Hint:

Angular velocity is measured in radians per second and is obtained by dividing the total rotation angle by the time taken for one complete revolution.

Answer 1

Answer: (E)

The second hand of an analog clock completes one full revolution (\( 2\pi \) radians) in 60 seconds. 
The angular velocity \( \omega \) is calculated as: \[ \omega = \frac{{\text{Total angle covered in radians}}}{{\text{Time taken}}} \] \[ \omega = \frac{2\pi}{60} = \frac{\pi}{30} \, \text{rad/s} \] Thus, the angular velocity of the second hand is \( \frac{\pi}{30} \) rad/s.