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

w = 7.27 x 10-5 rad/s

v = 467.99 m/s

Step-by-step explanation:

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

Angular Velocity =w= Angular Distance

Time

Angular distance covered 1 rotation = 2π

radians

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

Therefore,

2π rad 86400 s 3

w = 7.27 x 10-5 rad/s

Now, for the linear velocity:

v = rw

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