Spin out! An interesting amusement park activity involves a cylindrical room that spins...

Spin out! An interesting amusement park activity involves a cylindrical room that spins about a vertical axis (Fig. P5.26). Participants in the “ride” are in contact with the wall of the room, and the circular motion of the room results in a normal force from the wall on the riders. When the room spins sufficiently fast, the floor is retracted and the frictional force from the wall keeps the people “stuck” to the wall. Assume the room has a radius of 2.0 m and the coefficient of static friction between the people and the wall is

(a) Draw pictures showing the motion of a “rider.” Give both a side view and a top view.

(b) What are all the forces acting on a rider? Add them to your pictures in part (a). Then draw a free-body diagram for a rider.

(c) What are the components of all the forces directed toward the center of the circle (the radial direction)?

(d) Apply Newton’s second law along both the vertical and the radial directions. Find the minimum rotation rate for which the riders do not slip down the wall.