Question

The angular velocity of earth about its axis of rotation is:

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

Answer 1

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

The average angular velocity of an object can be represented by the following equation:

$\omega average=\frac{\Delta \theta }{\Delta t}$

where

ω is the radians/revolutions per second (on average),

$\Delta$ is the change in quantity,

$\theta$ is the velocity, and

t is time.

When calculating the angular velocity of the Earth as it completes a full rotation on its own axis (a solar day),

this equation is represented as:

${\omega }_{avg}=\frac{2\pi rad}{1day}$

$\therefore {\omega }_{avg}=\frac{2\pi }{60\times 60}rad/sec$