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

The angular speed of the Earth is approximately
`7.292* 10^(-5)` radians per second.

Step-by-step 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 = (2\pi)/(T)` (Eq. 1)

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

Therefore, the angular speed of the planet is:

`\omega = (2\pi)/(23\,h* (3600\,s)/(1\,h)+56\,min* 60\,(s)/(min)+4\,s )`

`\omega \approx 7.292* 10^(-5)\,(rad)/(s)`

The angular speed of the Earth is approximately
`7.292* 10^(-5)` radians per second.