Chapter 10, Problem 69PP

Human moment of inertia. The moment of inertia of the human body about an axis through its center of mass is important in the application of biomechanics to sports such as diving and gymnastics. We can measure the body’s moment of inertia in a particular position while a person remains in that position on a horizontal turntable, with the body’s center of mass on the turntables rotational axis (Figure 10.80). The turntable with the person on it is then accelerated from rest by a torque produced by using a rope wound around a pulley on the shaft of the turntable. From the measured tension in the rope and the angular acceleration, we can calculate the body’s moment of inertia about an axis through its center of mass.

Figure 10.80

Problems 69-72.

69. The moment of inertia of the empty turntable is 1.5 kg·m². With a constant torque of 2.5 N·m, the turntable–person system takes 3.0 s to spin from rest to an angular speed of 1.0 rad/s. What is the person’s moment of inertia about an axis through her center of mass? Ignore friction in the turntable axle.