Question

In: Physics

A 2.2 kg hoop 1.2 in diameter is rolling to the right without slipping on a...

A 2.2 kg hoop 1.2 in diameter is rolling to the right without slipping on a horizontal floor at a steady 2.6 rad/s. A uniform cylinder with its outer radius two times it’s inner radius with the same mass, same diameter as the hoop and also rolls without slipping with the same angular frequency. What is the ratio of rotational kinetic energies between the hoop and the uniform cylinder? What is the ratio of the rotational frequency between the hoop and uniform cylinder for the two to rotate with the same angular momentum about an axis through their center of mass?

Expert Solution

The mass of hoop =, radius of hoop = ,angular frequency of hoop =

Moment of inertia of hoop

Rotational kinetic energy of hoop

The mass of cylindrical shell = ,Outer radius of cylindrical shell , Inner radius of cylindrical shell ,

Moment of inertia of cylinder

Rotational kinetic energy of cylinder is

Ratio of rotational kinetic energies of hoop and cylinder is

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If the hoop and cylinder has same angular momentum,

Ratio of rotation frequency between the hoop and cylinder is

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genius_generous answered 3 years ago

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