Question

The angular velocity of the minute hand and the second hand is?

• A. Same
• B. Minute hand has higher angular velocity
• C. Second hand has higher angular velocity
• D. None of the above

Hint:

Angular velocity depends on the time taken for a complete rotation. The shorter the time, the higher the angular velocity.

Answer 1

The Correct Option is C

The angular velocity of a rotating object is defined as the rate at which the object moves through an angle. For a clock: - The minute hand completes one full rotation (360° or \( 2\pi \) radians) in 60 minutes. - The second hand completes one full rotation (360° or \( 2\pi \) radians) in 60 seconds. To compare angular velocities, we use the formula: \[ \omega = \frac{\Delta \theta}{\Delta t} \] Where: - \( \Delta \theta \) is the angular displacement (in radians), - \( \Delta t \) is the time interval. For the minute hand: \[ \omega_{\text{minute}} = \frac{2\pi}{60 \times 60} = \frac{\pi}{1800} \text{ radians per second} \] For the second hand: \[ \omega_{\text{second}} = \frac{2\pi}{60} = \frac{\pi}{30} \text{ radians per second} \] Clearly, the second hand has a higher angular velocity than the minute hand.
Thus, the correct answer is \( \text{Second hand has higher angular velocity} \).