The parallel axis theorem states that the moment of inertia of an object rotatin

Question

The parallel axis theorem states that the moment of inertia of an object rotating about an axis that is parallel to the center of mass is equal to the moment of inertia about the center of mass plus a Mh^2 term where h is the parallel distance away from the center of mass axis that the object is rotating around: I_parallel = I_COM + Mh^2. Calculate the moment of inertia of a 85 kg cylinder (which has the same I_COM as that of a solid disk with the same mass and radius) with a radius of 0.25 meters about an axis that is parallel to its center of mass and a distance of 1.5 meters away from it. Calculate the moment of inertia of a 85 kg point mass rotating around an axis 1.5 meters away. Using part a as the actual value, what percentage error does it induce to consider the cylinder as a point mass?

Explanation / Answer

a)

Icom = 0.5*MR^2

So, Inew= 0.5*MR^2 + Mh^2

So, Inew = 0.5*85*0.25^2 + 85*1.5^2

So, Inew = 193.9 kg.m2

b)

I = Icom + Mh^2

= MR^2 + Mh^2

= 85*0.25^2 + 85*1.5^2

= 196.6 kg.m2

c)

So, percentage error = (196.6 - 193.9 )/193.9

= 0.0139

= 1.39 percent

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