This is a rather neat mechanics problem (in my opinion at least):(adsbygoogle = window.adsbygoogle || []).push({});

A sphere with radius r and mass m sits on top of a cylinder with radius R and mass M that can rotate without friction about its axis (normal to the direction of gravity).

The sphere's moment of inertia with respect to an axis through its center (which also is its C.M) is given as: [tex]I_{s}=mk_{s}r^{2}[/tex].

The cylinder's moment of inertia with respect to its axis (on which its C.M is placed) is given by:

[tex]I_{c}=Mk_{c}R^{2}[/tex]

The problem:

The sphere is displaced from equilibrium, and begins rolling down the cylinder.

Find the angular velocity of the cylinder when the sphere loses contact with the cylinder

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# A rolling problem

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