A uniform disk of radius R=1m rotates counterclockwise with angular velocity ω=2rads/s about a fixed perpendicular axle passing through its center. The rotational inertia of the disk relative to this axis is I=9kg⋅m2. A small ball of mass m=1 is launched with speed v=4m/s in the plane of the disk and remains stuck to the disk after collision and the trajectory of the ball is d=0.5m above the horizontal axis. Neglect gravity and assume the axle is frictionless.
a) Find the angular velocity after the collision .
b) Compute the loss of kinetic energy during the collision.
L = Iω = r × p = m(r × v)
K = ½Iω2
K = mv2
The Attempt at a Solution
I have done a similar problem in which a ball is dropped on a disk rotating on a vertical axis in which case the ball does not cause any net torque. In this case the problem is simply L = (I+md2)ω which you can solve for ω. However, in this problem, the ball does cause a torque I attempted to use the same equation but I know this isn't the right way to do it. I can't find an example of this kind of problem anywhere online so hopefully someone here can help me.