# Angular momentum and oscillation of disk

1. Dec 17, 2007

### jonnyboy

[SOLVED] Angular momentum and oscillation of disk

A large solid disk of mass M and radius R is mounted on a fixed axis through its center using ideal bearings. A small projectile of mass m_1 traveling with velocity v_1 collides tangentially to the slight extension and sticks to the larger disk causing it to rotate about its center and oscillate

a. Determine the maximum angle the disk will rotate (theta_max)
b. Determine the frequency of oscillation ( assume theta_max is small enough so that the angle approximation is valid)

If someone would know what steps I need to take or where to start would be a great help.

Last edited: Dec 2, 2008
2. Dec 18, 2007

### Staff: Mentor

When the mass m1 with some momentum and kinetic energy impacts the disk of mass M, the disk will rotate to some angle at which the smaller mass is at some height (change in potential energy) where the rotation stops. Then the disk will rotate in the opposite direction, and oscillate.

So one has to determine by that appropriate conservation equation(s), the height at which m1 stops, and related that to the maximum angle of rotation.

Then one must determine the appropriate equation of motion from which one will obtain an expression for frequency.