Question

Debbie is in Los Angeles, at a distance r = 5280 km from the Earth’s axis of rotation.

(a) What is Debbie’s speed (as measured by an observer not moving relative to the center of the Earth)?

(b) What is Debbie’s acceleration? Your answer indicates to what extent the apparent acceleration due to gravity is modified when not at one of the poles. For reference, g = 9.81 m/s^2 at the poles, but appears slightly less near the equator.

Answer 1

a) Earth is rotating at an angular velocity 2pi radian or 360 degrees in 23 hour 56 min 4 sec. Hence

The apparent speed can be calculated by using formula

Tangential velocity

b) The acceleration due to gravity is modified because of the centrifugal force which is acting outward as

Hence the effective force on the body is

Hence the effective (modified) acceleration of gravity is

The value of is (see the first diagram)

(we are taking earth radius at equator as 6378 km)

Hencce the effectime gravitational acceleration is