The moment of inertia (sometimes referred to as a \"swing weight\") is a measure

Question

The moment of inertia (sometimes referred to as a "swing weight") is a measure of the resistance to rotation about a particular axis. It is often expressed as I_a = mk^2 _a where m is the mass of the object and k_a is the radius of gyration about the axis of rotation. In the following figure, the radius of gyration k_a for the arm about its COM = 0.36S*(arm length). Compute the moment of inertia of the arm in the extended position about its own COG. The arm weighs 5% of the body mass and the COM of the arm is 53% from the proximal joint

Explanation / Answer

The radius of gyration for an arm about it's COM is given as,

ka = (0.368) (arm length)

We know that, COM of an arm is 53% from the proximal joint.

then, we have

ka = (0.368) [(0.53) (0.58 m)]

ka = 0.1131232 m

The moment of inertia of an arm in the extended position about it's own COG will be given by,

Ia = m ka2

where, m = mass of human = 70 kg

Then, we get

Ia = [(0.05) (70 kg)] (0.1131232 m)2

Ia = 0.0447 kg.m2

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