Question

Find the angular velocity of the earth as it spins on its axis and the tangential velocity of an object at the equator AND one at the University of West Florida in Pensacola.

Answer 1

the tangential speed will be half the speed at the equator at the latitude where the circumference of the earth is half the equatorial circumfeence

with a little trig, you should be able to show that:

r=R cos(Theta) where R is the radius of the earth, theta is the latitude (angle north of the equator), and r is the radius of the circle described by the line of latitude at angle theta

so, for the circumference an object's rotation around the earth to be half the equatorial value, we have that cos(theta)=1/2, which occurs at theta = 60 deg

we know a person at the equator has an angular velocity of 2 pi rad/1day = 2pi rad/86,400s

all observers on the earth have the same ang velocity, since the earth rotates at the same rate at all latitudes...all observers on the surface of the earth complete 2 pi rad in 1 day