Question

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

Answer 1

The moment of inertia for a system of a rotating disk and its population is found by summing the individual moments of inertia for the disk, person, and dog, applying the parallel axis theorem as needed.

Step-by-step explanation:

To determine the moment of inertia of a system consisting of a horizontal platform (uniform disk) and its population (a person and a dog), we must consider the individual moments of inertia and apply the parallel axis theorem where necessary. The moment of inertia of a uniform disk about an axis through its center is given by ½MR², where M is the mass of the disk and R is its radius. If a person of mass m stands at a distance d from the center, their contribution to the moment of inertia can be represented as md². Similarly, for a dog of mass m_dog placed at a distance d_dog, the contribution would be m_dog*d_dog². The total moment of inertia of the system is the sum of the moments of inertia of the platform, person, and dog.