Question

In: Physics

A uniform solid sphere with Radius R has KE (rotational) at an angular speed of w...

A uniform solid sphere with Radius R has KE (rotational) at an angular speed of w when spinning about an axis through its center. A uniform thin-walled hollow shell of radius 2R has 1/3 KE (rotational) at an angular speed of w when spinning about an axis through its center. If m=M for solid sphere, whats the mass of the hollow sphere?

Expert Solution

Given the uniform solid sphere has a mass of M and radius R rotating with an angular speed and spinning about an axis through its centre. Its rotationak kinetic energy is given by,

The moment of inertia I of a solid sphere about an axis passing through its centre is,

Therefore,

For the hollow solid sphere of mass M' and radius R'= 2R rotating with an angular speed and spinning about an axis through its centre. Its rotationak kinetic energy is given by,

The moment of inertia I' of a solid sphere about an axis passing through its centre is,

Therefore,

Given,

So the mass of the hollow sphere is 1/20 times the mass of the solid sphere.

genius_generous answered 3 years ago

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