Question

The earth rotates through one complete revolution every 1,440 minutes. Since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 1440 minutes. Find the angular velocity of a person standing on the equator.

Answer 1

Answer:

The angular velocity of a person standing on the equator is approximately $7.272\times 10^{-5}$ radians per second.

Explanation:

The Earth rotates at constant speed. From Rotational Physics, the angular velocity ($\omega$), measured in radians per second, is defined by the following formula:

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

Where $T$ is the period of rotation of the Earth, measured in seconds.

If we know that $T = 86400\,s$, then the angular velocity of a person standing on the equator is:

$\omega = \frac{2\pi}{86400\,s}$

$\omega \approx 7.272\times 10^{-5}\,\frac{rad}{s}$

The angular velocity of a person standing on the equator is approximately $7.272\times 10^{-5}$ radians per second.