Question

List all the possible formulas that could be used for the following scenario. Chapters from chapters Motion in a cirlce, torque, gravity.

"In the winter Olympics, skaters go around the curved part of a flat oval track at top speed without sliding."

Answer 1

You'll probably need the following formulas:

1) Calculate downward force on the skater due to gravity. We can take upward direction as Y-axis:

, where m is the mass of the skater

2) In the horizontal direction, the contact force is provided by centripetal acceleration, a_c. Taking horizontal direction as X-axis:

The centripetal acceleration is

where v is the velocity of center of mass of the skater and R is the radius of the curved path.

Thus,

3) Because the curved part of the track is flat, the skater has to lean inward because of centripetal acceleration. Suppose the angle of leaning is Let the center of mass of the system be at point G in the figure. D is the distance between point O and G.

We can next calculate Since the skater is not rotating, is constant for the curved part, and hence the moment about the center of mass is zero. We can write this as:

or