Moment of inertia is a scalar. Therefore, if several objects are connected toget

Question

Moment of inertia is a scalar. Therefore, if several objects are connected together, the moment of inertia of this compound object is simply the scalar (algebraic) sum of the moments of inertia of each of the component objects. Use this principle to answer each of the following questions about the moment of inertia of compound objects:

Part A: A solid uniform wooden cylinder has mass and radius . To make this object suitable for a machine part, you need to increase its moment of inertia about an axis though its center perpendicular to its faces. To do this, you add a very thin layer of an extremely dense metal to the outside of the cylinder, so that the radius of the cylinder will not change appreciably. What mass of metal (in terms of ) must you add to double the cylinder's moment of inertia?
Answer : m/2


Part B: A uniform solid wooden sphere of mass and radius is spinning about an axis through its center. In order to meet weight specifications, its mass needs to be increased without changing its size. This is done by adding a very thin uniform coating of a dense metal foil to the outer surface of the sphere. Such a coating will not appreciably change the diameter of the sphere. If you add enough of this foil to double the sphere's mass, what is the ratio of its new moment of inertia to the moment of inertia of the original wooden sphere without the foil?

I need help with the last question please.

Explanation / Answer

Inew/Iold=2:1

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