You are given a heavy but thin metal disk (like a coin, but larger; see figure b

Question

You are given a heavy but thin metal disk (like a coin, but larger; see figure below) that has a mass of 0.59 kg and a radius of 0.13 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 0.26 m and a mass equal to 0.82 kg and rotates on a frictionless bearing. The disk has an initial angular speed of 30 rev/min. (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?

Explanation / Answer

0.03 . 33 = ( 0.03 + 1.11 . 0.1^2) . X X = 0.99 / 0.0411 = 24.087 = 24.1 rpm

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