Question

A biomechanics lab student measured the length of his leg from hip to heel at .9m. What is the frequency of the pendulum motion of the student's leg? What is the period? (The moment of inertia for a leg is about I=1/3 * m * L^2. The center of gravity/mass is at the midpoint.)

Answer 1

Solution:

Let us go to the basics first.

We can model a human leg reasonably well as a rod of uniform cross section, pivoted at one end (the hip).

Moment of inertia, I of a rod pivoted about its end is (1/3)mL^2. The center of gravity of a uniform leg is at the midpoint, so d = L/2.

The frequency of a physical pendulum is given by

f = (1/2π)√(mgd/I)

=> f = (1/2π)√[mg(L/2) / {(1/3)mL^2}]

=> f = (1/2π)√[g(1/2) / (1/3)L]

=> f = (1/2π)√[(g/2) / (L/3)]

=> f = (1/2π)√[(3/2)(g/L)]

=> f = (1/2*3.14)√[(3/2)(9.8/0.9)]

=> f = 0.64 Hz (Answer => Frequency)

Time period, T = 1 / f = 1 / 0.64 = 1.6 Seconds (Answer)