A thin hoop of mass M and radius R is suspended from a string through a point on the rim of the hoop. If the support is turned with high angular velocity w, the hoop will spin as shown, with its plane nearly horizontal and its center nearly on the axis of the support. The string makes angle a with the vertical. The center of mass of the hoop precesses around the vertical at rate w. Draw the free body diagram for the hoop. Find the total angular velocity in cylindrical coordinates (i.e., in î , k . and ô notations) Find, approximately, the small angle ß between the plane of the hoop and the horizontal. (for small angles sin ß ß and cos ß × 1)

A thin hoop of mass M and radius R is suspended from a string through a point on the rim of the hoop. If the support is turned with high angular velocity w, the hoop will spin as shown, with its plane nearly horizontal and its center nearly on the axis of the support. The string makes angle a with the vertical. The center of mass of the hoop precesses around the vertical at rate w. Draw the free body diagram for the hoop. Find the total angular velocity in cylindrical coordinates (i.e., in î , k . and ô notations) Find, approximately, the small angle ß between the plane of the hoop and the horizontal. (for small angles sin ß ß and cos ß × 1)