Question

Calculate the angular velocity of the following arms of the clock in rad/sec.

• A. $\frac{\pi }{30}$
• B. $\frac{\pi }{21600}$
• C. $\frac{\pi }{1800}$

Answer 1

We know that second's hand completes its revolution $\left(2\pi \right)$ in 60 sec $\therefore \omega =\frac{\theta }{t}=\frac{2\pi }{60}=\frac{\pi }{30}$ rad/sec
For minute's hands, it takes 3600sec to complete one revolution.
$\therefore \omega =\frac{\theta }{t}=\frac{2\pi }{3600}=\frac{\pi }{1800}$ rad/sec
For hour's hands, it takes 43200sec (12 hrs) to complete one revolution.
$\therefore \omega =\frac{\theta }{t}=\frac{2\pi }{43200}=\frac{\pi }{21600}$ rad/sec