A gyroscope consists of a rotating disk with a 25 cm radius suitably mounted at the midpoint of a 20 cm long axle so that it can spin and precess freely. One end is supported by a stand. The disk spins at 2000 rpm. The mass of the disk is 2 kg, and the axle can be taken as massless. Required:
a. Draw the gyroscope, indicating the direction of the initial angular speed and the initial angular momentum. Choose a direction for the spin of the disk.
b. Draw the torque due to gravity about the support point.
c. What direction will your gyroscope precess once you release it?
d. Find the time required for one precession of the gyroscope if it is supported at one end of the axle and it precesses in the horizontal plane.