Question

The angular velocity of earth about its axis of rotation is

• A. $\frac{2\pi }{(60\times 60\times 24)}\text{rad/sec}$
• B. $\frac{2\pi }{(60\times 60)}\text{rad/sec}$
• C. $\frac{2\pi }{60}\text{rad/sec}$
• D. $\frac{2\pi }{(365\times 24\times 60\times 60)}\text{rad/sec}$

Answer 1

The correct option is A $\frac{2\pi }{(60\times 60\times 24)}\text{rad/sec}$

As we know, angular velocity $\omega =\frac{2\pi }{t}\text{rad/sec}$
Since, earth completes one rotation in $24\text{hours}$ about its own axis,
So, $t=24\text{hours}=24\times 60\times 60\text{seconds}$

$\therefore \omega =\left(\frac{2\pi }{60\times 60\times 24}\right)\text{rad/s}$