Question

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 turntable's rotational axis. The turntable with the person on it is then accelerated from rest by a torque that is 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. 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 of1.0 rad/s. What is the person’s moment of inertia about an axis through her center of mass? Ignore friction in the turntable axle.

Answer 1

The moment of inertia of the human body can be measured by placing the person on a horizontal turntable and accelerating the turntable using a torque produced by a rope wound around a pulley on the shaft. From the measured tension in the rope and the angular acceleration, we can calculate the body's moment of inertia about its center of mass.

Step-by-step explanation:

The moment of inertia of the human body can be measured by placing the person on a horizontal turntable and accelerating the turntable using a torque produced by a rope wound around a pulley on the shaft. From the measured tension in the rope and the angular acceleration, we can calculate the body's moment of inertia about its center of mass. In this case, the moment of inertia of the empty turntable is given as 1.5 kg·m².

To find the person's moment of inertia, we can use the equation:

I = (T - I_turntable * α) / α

Where T is the torque, I_turntable is the moment of inertia of the turntable, and α is the angular acceleration. In this case, the torque is 2.5 N·m, the angular acceleration is calculated using the given time and final angular speed, and the moment of inertia of the turntable is 1.5 kg·m².

After substituting the values into the equation, we can calculate the person's moment of inertia.