Interestingly, there have been several studies using cadavers to determine the moment of inertia of human body parts by letting them swing as a pendulum about a joint. In one study, the center of gravity of a 5.0 kg lower leg was found to be 18 cm from the knee. When pivoted at the knee and allowed to swing, the oscillation frequency was 1.6 Hz.

Question

Interestingly, there have been several studies using cadavers to determine the moment of inertia of human body parts by letting them swing as a pendulum about a joint. In one study, the center of gravity of a 5.0 kg lower leg was found to be 18 cm  from the knee. When pivoted at the knee and allowed to swing, the oscillation frequency was 1.6 Hz.
What was the moment of inertia of the lower leg?

drwls · Answer

Such a measurement would provide a moment of inertia about the knee joint.

This a standard "physical pendulum" problem.
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/SHM/PhysicalPendulum.html
The frequency is
f = [1/(2 pi)] sqrt [m*g*L/I]
where L is the distance from joint (knee) to CM and m is the mass.

Solve for I

Anonymous · Answer

.0087