Question

A 113kg horizontal platform is a uniform disk of radius 1.89m and can rotate about the vertical axis through its center. a 69.1kg person stands on the platform at a distance of 1.19m from the center, and a 27.1kg dog sits on the platform near the person 1.39m 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

To find the moment of inertia of the system consisting of the platform and its population with respect to the axis, you need to consider the contributions of each object. The total moment of inertia is the sum of the individual moments of inertia of the platform, the person, and the dog.

Step-by-step explanation:

To find the moment of inertia of the system consisting of the platform and its population with respect to the axis, we need to consider the contributions of each object. The moment of inertia of a uniform disk is given by I = (1/2)MR^2, where M is the mass and R is the radius.

For the platform, I-platform = (1/2)(113 kg)(1.89 m)^2.

For the person, I-person = M-person * (distance from axis)^2 = (69.1 kg)(1.19 m)^2.

For the dog, I-dog = M-dog * (distance from axis)^2 = (27.1 kg)(1.39 m)^2.

The total moment of inertia of the system is the sum of these individual moments of inertia: I-total = I-platform + I-person + I-dog.