Find the centripetal accelerations of (a) a point on the equator of the earth and (b) a point at the north pole of the earth.

Earth rotate about its axis which passes through its center

centripetal acceleration a = rw²

r is the radius of earth

(a) radius at equator r = 6.37 x 10⁶ m

w is the angular speed

w = 2*п/T

T is the time period to complete one rotation

T = 24 hours = 24x60x60 sec

T = 86400 sec

w = 2*3.14/86400

w = 7.27 x 10⁻⁵ rad/sec

a = rw²

a = (6.37 x 10⁶)(7.27 x 10⁻⁵)²

a = 3.37 x 10⁻² m/s²

(b) radius of earth from axis of rotation at pole is zero

r=0

so angular acceleration at pole =0

double the distance = divide strength by 4