Question

Interestingly, there have been several studies using cadavers to determine the moments of inertia of human body parts, information that is important in biomechanics. In one study, the center of mass of a 5.7 kg lower leg was found to be 18 cm from the knee. When the leg was allowed to pivot at the knee and swing freely like a pendulum, the oscillation frequency was 1.7 Hz.
What was the moment of inertia of the lower leg?

Answer 1

Answer:

0.08821 kgm²

Explanation:

f = Frequency = 1.7 Hz

m = Mass of lower leg = 5.7 kg

d = Distance of center of mass = 18 cm

g = Acceleration due to gravity = 9.81 m/s²

I = Moment of inertia

Frequency is given by

$f=\frac{1}{2\pi}\sqrt{\frac{mgd}{I}}\\\Rightarrow I=\frac{mgd}{(2\pi f)^2}\\\Rightarrow I=\frac{5.7\times 9.81\times 0.18}{(2\pi 1.7)^2}\\\Rightarrow I=0.08821\ kgm^2$

The moment of inertia of the lower leg is 0.08821 kgm²