# Homework Help: Rotational Dynamics of two disks

1. Nov 5, 2013

### Nicolaus

1. The problem statement, all variables and given/known data
Two disks are spinning freely about axes that run through their respective centres (see figure below). The larger disk
(R1 = 1.42 m)
has a moment of inertia of 1070 kg · m2 and an angular speed of 4.2 rad/s. The smaller disk
(R2 = 0.60 m)
has a moment of inertia of 909 kg · m2 and an angular speed of 8.0 rad/s. The smaller disk is rotating in a direction that is opposite to the larger disk. The edges of the two disks are brought into contact with each other while keeping their axes parallel.

They initially slip against each other until the friction between the two disks eventually stops the slipping. How much energy is lost to friction? (Assume that the disks continue to spin after the disks stop slipping.)

2. Relevant equations
Conservation of angular momentum.

3. The attempt at a solution
I attempted the problem by first using the cons. of angular momentum to find the final angular speed of the 2 disks, then subtracted the initial kinetic energy by the final kinetic energy of the system to obtain energy lost, though I apparently arrived at the wrong answer. What is the correct approach to this problem?

2. Nov 5, 2013

### Dick

You've got exactly the correct approach. You'll need to show your work for anyone to be able to tell you exactly where you went wrong.

3. Nov 5, 2013

### TSny

This is an interesting problem which I first saw many years ago in a textbook. The angular momentum is not conserved and it's a nice puzzle to see why.

You can introduce a friction force f that acts between the disks while they are slipping. Consider the torque due to the friction force on each disk. The answers for the final rates of spin are independent of the magnitude of f.

4. Nov 5, 2013

### Dick

Yeah, I guess I didn't give that one enough thought.

5. Nov 8, 2013

### Nicolaus

Are the final angular speeds going to be different for each disk? If that is the case, can I just use the cons. of angular momentum and the cons. of energy, and it becomes two equations with 2 unknowns, then isolate and solve for one of the angular speeds?

6. Nov 8, 2013

### TSny

Right, the final angular speeds are going to be different. What will be the same for the two disks when slipping stops?

Neither total kinetic energy nor total angular momentum will be conserved.