Question

1. 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 Ia = mka2 where m is the mass of the object and ka is the radius of gyration about the axis of rotation.
The radius of gyration ka for the arm about its COM = 0.368*(arm length). Compute the moment of inertia of the arm in the extended position about its own COG. The mass of the human is 70 kg total.

Joint	X (cm)	Y (cm)
Shoulder	0	0
Wrist	58	0

The arm weighs 5% of the body mass and the COM of the arm is 53% from the proximal joint.

2. Compute the moment of inertia of the arm about the shoulder joint using the parallel axes theorem. Parallel axes theorem Ia = Icg + mr2

Answer 1

1. mass = 0.05 M = 0.05 x 70 = 3.5 kg

Icm = m K^2

= (3.5)(0.368 x 0.58)^2

= 0.16 kg m^2 .......Ans

2. I = Icm + m d^2

d = 0.53 x 0.58 m = 0.3074 m

I = (0.16) + (3.5)(0.3074^2)

I = 0.49 kg m^2