You\'re sitting in a chair that can rotate freely about a vertical axis. The mom

Question

You're sitting in a chair that can rotate freely about a vertical axis. The moment of inertia of you and the chair (together as one object) about that axis is Ic. Initially, you and the chair are at rest. But you're holding a disk whose axis of rotation aligns with the axis of the chair. The disk's moment of inertia about its axis is ID. The disk is initially at rest. You then use your free hand to start the disk spinning on its axis at a velocity of omega D. As a result, you and the chair also begin to rotate together, with an angular velocity omega C. If omega D/omega C = x, what is Id/IC ?

Explanation / Answer

angualr momentum willl be conserved so 0 = Id Wd + Ic Wc Id/Ic = -Wc/Wd = -1/x

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