Question

It takes 23 hours 56 minutes and 4 seconds for the earth to make one revolution (mean sidereal day). What is the angular speed of the earth

Answer 1

Answer:

The angular speed of the Earth is approximately $7.292\times 10^{-5}$ radians per second.

Explanation:

We suppose that Earth rotates at constant angular speed. From Rigid Body Physics, we remember that angular speed of the planet ($\omega$), measured in radians per second, is:

$\omega = \frac{2\pi}{T}$ (Eq. 1)

Where $T$ is the period, measured in seconds.

Therefore, the angular speed of the planet is:

$\omega = \frac{2\pi}{23\,h\times \frac{3600\,s}{1\,h}+56\,min\times 60\,\frac{s}{min}+4\,s }$

$\omega \approx 7.292\times 10^{-5}\,\frac{rad}{s}$

The angular speed of the Earth is approximately $7.292\times 10^{-5}$ radians per second.