Question

 What is the angular velocity of earth?
A. \[\dfrac{{2\pi }}{{86400}}rad/\sec \]
B. \[\dfrac{{2\pi }}{{3600}}rad/\sec \]
C. \[\dfrac{{2\pi }}{{24}}rad/\sec \]
D. \[\dfrac{{2\pi }}{{6400}}rad/\sec \]

Answer 1

Hint:As it is a basic fact that the time taken by earth to complete 1 rotation is 24 hours and the angular frequency of earth can be find using the formula i.e. frequency = 1/(time taken to complete 1 revolution) using this formula we can find the angular velocity of earth.

Complete step by step answer:
To complete 1 rotation earth takes 24 hours
Therefore time taken by earth to complete 1 rotation= t = 24 hours = $24 \times 60 \times 60$ = 86400 secs
Frequency of the rotation of earth = f = \[\dfrac{1}{t}\] = \[\dfrac{1}{{86400}}{\sec ^{ - 1}}\]
Angular velocity of earth \[ = \omega = 2\pi f = \dfrac{{2\pi }}{{86400}}rad/\sec \]
Therefore \[\dfrac{{2\pi }}{{86400}}rad/\sec \] is the angular velocity of earth.

Note: In these types of questions while calculating the angular velocity of earth to complete 1 rotation this equation is represented as: \[{\omega _{avg}} = \dfrac{{2\pi}}{{86400}}rad/\sec\] which results of $7.2921159 \times {10^{ - 5}}rad/\sec$ or we can easily find the angular velocity of earth by simply finding the angular frequency of earth.