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?

In the figure, a solid cylinder attached to a horizontal spring (k = 9.00 N/m) rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) If the cylinder has mass M = 5.30 kg, find the period of the simple harmonic motion that the cylinder's center of mass executes. (Hint: Find the time derivative of the total mechanical energy.) (a) Number i Units (b) Number i Units (c) Number i Units >

A uniform stick of length L and mass m is pivoted at one of its ends. Derive an equation for the period of oscillation when the stick is set into small oscillation. Answer in terms of m, g, and L as needed.

Phy