Final answer:
The moment of inertia of the lower leg about the knee joint can be found using the period of a physical pendulum formula and the given values for the mass, distance to the center of mass, and oscillation frequency of the leg.
Step-by-step explanation:
The question asks us to determine the moment of inertia of the lower leg about the knee joint, given that the leg is used as a pendulum with an oscillation frequency of 1.4 Hz and a center of mass 16 cm from the knee. To find the moment of inertia (I), we can use the formula for the period of a physical pendulum: T = 2π√(I/mgh), where T is the period, m is the mass of the leg, g is the acceleration due to gravity, and h is the distance from the pivot to the center of mass. We know that the frequency (f) is the reciprocal of the period (T), so f = 1/T. Plugging in the values given, we can rearrange for I and find I = mgh/(4π²f²). Using the given values m = 4.1 kg, h = 0.16 m, and f = 1.4 Hz, and taking g to be approximately 9.81 m/s², we get I = 4.1 kg × 9.81 m/s² × 0.16 m / (4π² × (1.4 Hz)²), which gives us the moment of inertia of the lower leg about the knee joint.