The earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. Assuming the earth is a sphere with a radius of 6.38 x 106 m, determine the centripetal acceleration of a person situated (a) at the equator and (b) at a latitude of 52.0 ° north of the equator.

Question

Drew · Answer

What do we know?
r=6.38x10^6m
T=1 day=86,400s

Part A:
T=2(pi)r/V ==> V=2(pi)r/T
a=V^2/r (Plug & chug)

Part B:
Now, what do we know?
Only T=1 day=86,400s. We no longer know r.

Latitude we'll say is represented by "l".

So r(l) = r cos l

Once you find that radius, you follow the same series of equations as Part A.