A roller coaster car moves in a vertical circle of radius R. At the top of the circle the car has speed v1, and at the bottom of the circle it has speed v2, where v2>v1. Suppose that v2 is in the x-direction, and y-axis is directed upward.

1) When the car is at the top of its circular path, what is the direction of its radial acceleration, arad, top? The direction angle β-top of the radial acceleration arad, top is measured from the +x-direction toward the +y-direction.

2) When the car is at the bottom of its circular path, what is the direction of its radial acceleration, arad, bottom? The direction angle β-bottom of the radial acceleration arad, bottom is measured from the +x-direction toward the +y-direction.

3) In terms of v1 and v2, what is the ratio arad, bottom/arad, top?