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Question

A uniform circular disc of mass 50kg and radius 0.4m is rotating with an angular velocity of 10rads1 about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25kg and radius 0.2m, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rads1) of the system is:

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Solution

Conservation of angular momentum about vertical axis of disc
50(0.4)22×10=[50(0.4)22+2×2(6.25)(0.2)2]ω
ω=8 rad/sec

NOTE: The moment of inertia for the rings will be 2mR2 each. Because the axis will be at the circumference.

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