Question

Earth has a radius of 6.38× 106 m and rotates with a period of 23.9 hours. Find the speed of an object (a) on the equator and (b) in Las Vegas (latitude: 36.2° north).

Answer 1

r = radius of earth = 6.38× 10⁶ m

T = time period = 23.9 hours = 23.9 x 3600 sec

w = angular speed of rotation = 2 $\pi$ / T = 2 x 3.14 / (23.9 x 3600) = 0.000073 rad/s

a)

at equator

r = radius of horizontal circle = R Cos $\lambda$                       $\lambda$ = angle of lattitude

at equator , $\lambda$ = 0

so r = R = 6.38 × 10⁶ m

V = r w = R w = 6.38 × 10⁶ x 0.000073 = 465.74 m/s

b)

at Las vegas

r = radius of horizontal circle = R Cos $\lambda$                       $\lambda$ = angle of lattitude

at las vegas , $\lambda$ = 36.2

so r = R Cos36.2= 6.38 × 10⁶ Cos36.2 = 5.14 x 10⁶ m

V = r w = R w = 5.15 × 10⁶ x 0.000073 = 375.95 m/s