Short-track speed skating

In short-track skating, athletes go around an oval track which is small enough to fit inside a regulation hockey rink. The distance around the inner edge of the oval is L = 111 m.

1. What is the radius of curvature R of the inner oval of the track?

The skaters lean way, way over as they speed around the curves. Although they often place one hand on the ice for balance, they usually don't press down very hard on their fingertips.

1. Estimate the angle at which these skaters are leaning -- that is, how far above the horizontal is the line connecting their blades and their center of mass?

Assume that the skaters are at this moment moving in a circular path with constant speed.

2. Draw a free-body diagram showing all forces acting on a skater. Ignore the fingertip touching the ice.
3. Make a table showing the x-component and y-component of each force.
4. Figure out the size of the ice's horizontal (= centripetal) force on the skater. Your answer should have a factor of m for the mass of the skater.
5. Figure out the size of the centripetal acceleration of the skater. Your answer should NOT have a factor of m any more.
6. Based on this analysis, how fast are these skaters moving in the turn?
7. If they kept this same speed for an entire lap, how long would one lap take?
8. The best male skaters can complete a lap in a bit more than 9 seconds. Does this agree with your estimate? If not, does it still make sense?