Angular Velocity of Seconds Hand – Rankers Physics

Kinematics of Circular Motion: Practice Problem & Solution

Assertion (A): Angular velocity of the seconds hand of a watch is \(\frac{\pi}{30}\text{ rad/s}\). Reason (R): Angular velocity is equal to \(\frac{2\pi}{\text{T}}\) where \(\text{T}\) is the time period.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Kinematics of Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:

Angular velocity \(\omega = \frac{2\pi}{\text{T}}\). For a seconds hand, \(\text{T} = 60\text{ s}\). Thus, \(\omega = \frac{2\pi}{60} = \frac{\pi}{30}\text{ rad/s}\). Both assertion and reason are true, and the reason correctly explains the assertion.

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