If each of the following objects have the same mass, M, the same radius, R, and

Question

If each of the following objects have the same mass, M, the same radius, R, and are rotating with the same angular velocity,, which would come to rest in the shortest time when applying the same torque to each object. Remember you can look up things you need from tables in the chapter.

A) A hollow sphere spinning about an axis passing through the center.

B)An empty hollow can (with the top and bottom removed) spinning about an axis located at the center. line.

C)A solid thin bar of length L = 2R rotating about a point half-way along its length.

D)A solid thin bar of length L = 2R rotating about a point at one end of the bar.

Explanation / Answer

rotatinal energy = 1/2 Iw^2

I for hollow sphere = 2/3 * MR^2

I = 1/3*MR^2w^2

b ) empty hollow can like thin hollow cylinder

I = MR^2

c ) solid thin bar rotating axis point half way = I = ML^2/12 = 4MR^2/12 = MR^2/3

d ) solid thin bar rotating about a point at one end = I = ML^2/3 = 4MR^2/3

radius of gyration order

can > solid bar rotaing a point at one end of the bar > hollow sphere = solid lenght bar rotating about a point hhalf way along its lenght

can will stop in shortest time becausye it has more moment of inertia tan other objects

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