The parallel axis theorem provides auseful way to calculate the moment of inerti

Question

The parallel axis theorem provides auseful way to calculate the moment of inertia I about anarbitrary axis. The theorem states that I =Icm + Mh2, whereIcm is the moment of inertia of the objectrelative to an axis that passes through the center of mass and isparallel to the axis of interest, M is the total mass ofthe object, and h is the perpendicular distance betweenthe two axes. Use this theorem and information to determine themoment of inertia (kg·m2) of a solid cylinder ofmass M = 7.20 kg and radius R = 6.90 m relativeto an axis that lies on the surface of the cylinder and isperpendicular to the circular ends.

Explanation / Answer

The theorem:     I = Icm +MR2 With the cylinder:     Icm =(1/2)MR2                                h =R Thus,    I = (1/2)MR2 +MR2               =(3/2)MR2               =(3/2)*7.2*6.92 = 514.2 kg.m2               =(3/2)*7.2*6.92 = 514.2 kg.m2

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