Rotational Dynamics

1) How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.3 cm and a mass of 15.1 g. The laser scans at a constant tangential velocity of 1.26 m/s. Assume that the music is first detected at a radius of 20.3 mm from the center of the disk. Ignore the small circular hole at the CD's center.

2) A uniform diving board, of length 5.0 m and mass 52 kg, is supported at two points; one support is located 3.4 m from the end of the board and the second is at 4.6 m from the end (see the figure below). What are the forces acting on the board due to the two supports when a diver of mass 64 kg stands at the end of the board over the water? Assume that these forces are vertical. [Hint: In this problem, consider using two different torque equations about different rotation axes. This may help you determine the directions of the two forces.]

3) A turntable of mass 4.64 kg has a radius of 0.086 m and spins with a frequency of 0.530 rev/s. What is its angular momentum? Assume the turntable is a uniform disk.

4) A solid sphere of mass 0.595 kg rolls without slipping along a horizontal surface with a translational speed of 5.16 m/s. It comes to an incline that makes an angle of 35° with the horizontal surface. Neglect energy losses due to friction.

(a) What is the total energy of the rolling sphere?

(b) To what vertical height above the horizontal surface does the sphere rise on the incline?