Help finding final angular speed of a heavy metal disk?

Question

You are given a heavy but thin metal disk (like a coin, but larger; see figure below) that has a mass of 0.47 kg and a radius of 0.106 m. (Objects like this are called Euler disks.) Placing the disk on a turntable, you spin the disk, on edge, about a vertical axis through a diameter of the disk and the center of the turntable. As you do this, you hold the turntable still with your other hand, letting it go immediately after you spin the disk. The turntable is a uniform solid cylinder with a radius equal to 0.212 m and a mass equal to 0.7 kg and rotates on a frictionless bearing. The disk has an initial angular speed of 30 rev/min.

Picture with problem: http://i284.photobucket.com/albums/ll28/bathtub2008/10-59.gif

(a) The disk spins down and falls over, finally coming to rest on the turntable with its symmetry axis coinciding with the turntable. What is the final angular speed of the turntable?

______rad/s

(b) What will be the final angular speed of the turntable if the disk's symmetry axis ends up 0.100 m from the axis of the turntable?

______

Answer 1

Your question is inconsistent.

Both your words and the diagram have the edge of the vertical disk at the center of the turntable. That means that  the disk can't fall so that its center is at the center of the turntable.

Furthermore, you've said nothing about the coefficient of friction between the disk and the turntable. If there were no friction at all, then the disk would exert no torque on the turntable, the turntable would not start moving, and the disk would spin until first air friction and then its internal inelasticity caused it to come to rest.

If, on the other hand, there were friction between the disk and the turntable, then both would experience a torque, But again, because of air friction, there is no conservation of angular momentum here and, with friction, there is no conservation of energy either.

For more on Euler disks, you might want to look at:

http://en.wikipedia.org/wiki/Euler's_dis...

http://www.eulersdisk.com/physics.html