Moment of Inertia of Systems Video Lessons

Example

# Problem:  Suppose we want to calculate the moment of inertia of a 65.5 kg skater, relative to a vertical axis through their center of mass.Part (a). First calculate the moment of inertia (in kg-m2) when the skater has their arms pulled inward assuming they are cylinder of radius 0.135 m.Part (b). Now calculate the moment of inertia of the skater (in kg-m2) with their arms extended by assuming that each arm is 5% of the mass of their body. Assume the body is a cylinder of the same size, and the arms are 0.875 m long rods extending straight out from their body being rotated at the ends.

###### FREE Expert Solution

Moment of inertia of a cylinder:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{MR}}}^{{\mathbf{2}}}}$

Moment of inertia of a rod about the end:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{3}}{\mathbf{M}}{{\mathbf{L}}}^{{\mathbf{2}}}}$

Part (a).

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###### Problem Details

Suppose we want to calculate the moment of inertia of a 65.5 kg skater, relative to a vertical axis through their center of mass.

Part (a). First calculate the moment of inertia (in kg-m2) when the skater has their arms pulled inward assuming they are cylinder of radius 0.135 m.

Part (b). Now calculate the moment of inertia of the skater (in kg-m2) with their arms extended by assuming that each arm is 5% of the mass of their body. Assume the body is a cylinder of the same size, and the arms are 0.875 m long rods extending straight out from their body being rotated at the ends.