Question about velocities?

Question

I have a multiple choice question which asks, I am standing 1km south of the north pole and my friend is standing on the equator. Both are at sea level. As the earth rotates about its axis, you are both rotating with it. How do the angular and linear velocity of you and your friend compare? Pick one option below and justify your choice. Consider only the rotation of the earth on its axis and ignore its motion through space.

answers

a) linear velocities are the same. Angular velocity at the equator is much bigger than the angular velocity at the pole.

b) Both angular and linear velocities are much bigger at the equator than at the pole.

c) Both angular and linear velocities are much bigger at the pole than at the equator.

d) Angular velocities are the same. Linear velocity at the equator is much bigger than the angular velocity at the pole.

e) The linear velocities are the same. The angular velocity at the pole is much bigger than the angular velocity at the equator.

f)The angular velocities are the same. The linear velocity at pole is much bigger than the linear velocity at the equator.

Answer 1

The angular velocities are the same.  If the earth rotates 90º, both locations move through 90º.  However, the one at the equator moves much farther in the same time, so his velocity is higher,  The answer is d).

Consider the distance moved by each in one complete rotation of the earth.  The one at the equator moves the entire equatorial circumference which is 2πR, where R is the radius of the earth.  The one near the pole moves 2πr, where r is his distance (through the earth) from the axis, which is much less than R.

Answer 2

answer is D , but I think there is a typo: the linear velocity of at the equator is much larger than the linear velocity at the pole

linear velocity = angular velocity * distance from axis of rotation

The angular velocity of a rotating sphere is the same for any distance.  

Howerver, since the pole has a distance of zero from the axis of rotation (Earth rotates about pole), this means the linear velocity at the pole is zero.  

The linear velocity at the equator is the angular velocity times the radius of the earth.

This all means that the angular velocities are the same, and the linear velocity at the equator is larger than the linear velocity at the pole.