Question

A 101 kg horizontal platform is a uniform disk of radius 1.99 m and can rotate about the vertical axis through its center. A 61.3 kg person stands on the platform at a distance of 1.09 m from the center, and a 28.9 kg dog sits on the platform near the person 1.41 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.

Answer 1

The total moment of inertia for the system consisting of a platform, a person, and a dog is found by calculating the moments of inertia for each and summing them. The final moment of inertia for the entire system is 329.10 kg·m².

Step-by-step explanation:

To calculate the moment of inertia of the given system, consisting of a platform and its population (a person and a dog), we need to consider the moment of inertia of each component in the system. We will use the parallel axis theorem and the formula for the moment of inertia of a uniform solid disk.

1. Calculate the moment of inertia of the platform (Ip): Ip = (1/2)MR², where M is the mass of the disk, and R is its radius.
2. Use the parallel axis theorem to find the moment of inertia of the person (Iperson) and of the dog (Idog), where Iperson = mperson*rperson² and Idog = mdog*rdog². 'm' is the mass and 'r' is the distance from the rotational axis.
3. Add up the moments of inertia for the platform, the person, and the dog to get the total moment of inertia (Itotal).

Plugging in values:

• Ip = (1/2)(101 kg)(1.99 m)² = 199.00 kg·m²
• Iperson = (61.3 kg)(1.09 m)² = 72.55 kg·m²
• Idog = (28.9 kg)(1.41 m)² = 57.55 kg·m²
• Itotal = Ip + Iperson + Idog = 199.00 kg·m² + 72.55 kg·m² + 57.55 kg·m²
• Itotal = 329.10 kg·m²