Question

The earth rotates through one complete revolution every 24 hours. 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 24 hours. Find the angular and linear velocity of a person standing on the equator. The radius of earth is approximately 4000 miles.

Answer 1

Answer:

ω = 7.27 x 10⁻⁵ rad/s

v = 467.99 m/s

Explanation:

First, we will find the angular velocity of the person:

$Angular\ Velocity = \omega = \frac{Angular\ Distance}{Time}$

Angular distance covered = 1 rotation = 2π radians

Time = (24 h)(3600 s/ 1 h) = 86400 s

Therefore,

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

ω = 7.27 x 10⁻⁵ rad/s

Now, for the linear velocity:

$v = r\omega$

where,

v = linear velocity = ?

r = radius of earth = (4000 miles)(1609.34 m/1 mile) = 6437360 m

Therefore,

$v = (6437360\ m)(7.27\ x\ 10^{-5}\ rad/s)$

v = 467.99 m/s