Question

Consider a cylinder of mass M, radius R and length L. (a) Calculate the inertia tensor for rotations about the center of mass in the frame where the z axis is along the axis of the cylinder. Use cylindrical coordinates, where x = r cos θ and y = r sin θ. (b) Find the inertia tensor in the frame where the center of the “bottom side” is at the origin with the z axis along the axis of the cylinder. (c) Consider the limit of both cases above as R → 0. Do the results reduce to the expected values found in tables of “standard” moments of inertia? (d) Consider the limit as L → 0. Explain how we could have obtained this limit using the moment of inertia for a disk 1/2 MR^2 without having to perform any additional integrations.

Answer 1

Answer:

A cylinder of mass M,R is radius and L is length (a) the inertia tensor for rotations about the center of the mass in the frame .Use cylindrical coordinates x,y .(b) The inertia tensor in the frame where the center of the "bottom side" is at theorigin with z-axis.(C) the limit of the both cases above as R->0.(d) the moment of inertia for a disk1/2MR^2without having to perform any additional integrations.