The parallel axis theorem provides a useful way to calculate the moment of inert

Question

The parallel axis theorem provides a useful way to calculate the moment of inertia I about an arbitrary axis. The theorem states that I = Icm + Mh2, where Icm is the moment of inertia of the object relative to an axis that passes through the center of mass and is parallel to the axis of interest, M is the total mass of the object, and h is the perpendicular distance between the two axes. Use this theorem and information to determine the moment of inertia (kg·m2) of a solid cylinder of mass M = 8.80 kg and radius R = 9.90 m relative to an axis that lies on the surface of the cylinder and is perpendicular to the circular ends.

Explanation / Answer

Moment of inertia of solid cylinder with respect to center of mass Icm =(1/2)MR2

according to parallel axis thereom moment of inertia relative to an axis that lies on the surface of the cylinder

I =Icm + Mh2    hare h =distance between center and of cylinder to the surface =R

I =(1/2)MR2 + MR2 =(3/2) MR2

here M = mass of solid cylinder =8.80 kg , R =radius =9.90 m

I =(3/2)(8.80 kg)(9.90 m)2 =1293.73 kg m2

moment of inertia relative to an axis that lies on the surface of the cylinder is 1293.73 kg m2

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