What is the final angular speed?A uniform circular disk of radius R = 0.200 m and mass M = 1.00 kg rotates with angular speed wo = 10.0 radians/second on a frictionless pivot. A second disk, having half the radius of the first and made of the same material, is supported at rest a small distance above the first disk. When the small disk is dropped concentrically onto the larger disk, friction eventually causes the disks to reach a common angular speed.
I came up with 9.4 rad/s, which is correct.
What fraction of the initial rotational kinetic energy is converted to heat in the process?
I came up with .0588, which is also correct.
A motor must restore the angular speed of the combination to wo in one revolution. What torque must the motor supply ?
I used the equation [itex]\tau=I\alpha[/itex] here. I added each moment of inertia (for each disk individually):
The above I got using the standard formula for the moment of inertia for a disk (1/2)mr2.
Now I found the acceleration:
Then I multiplied the acceleration by the moment of inertia to come up with:
...however the above is incorrect. Could someone please tell me why? I have gone through my steps many times, meaning that the only way this could be wrong is if I took the wrong steps; my arithmetic is fine. I'd appreciate any input on this.
Thank you very much.