Show all your work. Each section is worth 5 points. You will be assigned partial credit based on the work you show. Including drawings and diagrams for the described situations. Note: If a picture, diagram, or givens are shared between your answers to different parts of the problem, you may state something like, “See part A for the diagram” rather than redoing that work. Make sure to explain why that work applies for the next section.

Diagram 1

Diagram 2

The big disk on the bottom has radius = 2r. In Diagram 1 the little disk on the top has radius = r. The top disk may be small, but it is very heavy. The top disk has twice the mass (2m) as the bottom disk (m). The bottom disk is spinning at ω when the top disk drops on to it. The top disk had no angular velocity when it was dropped.
Derive an equation for the angular velocity of both disks after the collision in terms of the given variables and any universal constants.
Derive an equation for the change in kinetic energy of the system as a result of the collision in terms of the given variables and any universal constants. If the change in kinetic energy is 0, state that and justify your answer.
The same experiment is duplicated with a new top disk with the same mass (2m) but double the radius (2r). Would the change in kinetic energy of the system be greater than, less than, or the same as the initial collision described in part A and B. Justify your answer in using physics principles, diagrams and equations.
The same experiment is duplicated with a solid spherical ball with a mass m and radius of r/5. The ball is dropped with 0 angular velocity at the very edge of the spinning lower disk and when it lands, it sticks to the disk. Would the change in kinetic energy of the system be greater than, less than, or the same as the initial collision described in part A and B. Justify your answer in using physics principles, diagrams and equations.