[pic] A solid, uniform cylinder with mass 8.25kg and diameter 15cm is spinning at 200 rpm on a thin, frictionless axle that stop the cylinder axis. You design a simple friction brake to stop the cylinder by pressing the brake against the outer rim with a normal force. The coefficient of kinetic friction between the brake and rim is 0.333. What must be the applied normal force to bring the cylinder to rest after it has turned through 5.25 rev?
[pic] A 2.2kg hoop 1.2m in diameter is rolling to the right without slipping on a horizontal floor at a steady 3 rad/s. (a) how fast is its center moving? (b) What is the total kinetic energy of the hip? (c) Find the velocity vector of each of the following points as viewed by a person at rest on the ground: i) the highest point on the hoop; ii) the lowest point on the hoop; iii) the point on the right side of the hoop, midway between the hoop and the bottom. (d) Find the velocity vector for each points in part c, except as viewed by someone moving along with same velocity as the hoop.
[pic] A solid ball is released from res and slides down a hillside that slopes downward at 65° from the horizontal. (a) What minimum value must the coefficient of static friction between the hill and ball surfaces have for no slipping to occur? (b) Would the coefficient of friction calculated in part a changed if the mass were doubled to 4kg?
[pic] A 392N wheel comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill it is rotating at 25 rad/s. The radius of the wheel is 0.6m, and its moment of inertia about its axis is 0.8MR2. Friction does work on the wheel as it rolls up the hill to a stop, a height h above the bottom of the hill; this work has absolute value 3500J. Calculate h.