Question 4

A cylinder has uniform density $\rho$, radius $R$ and height $h$. Without doing any calculations, draw a diagram showing a set of principal axes for rotations of the cylinder about its centre of mass.

Find the principal moments of inertia of the cylinder about its centre of mass.

The cylinder rotates about its centre of mass with angular velocity $\hbox{{\boldmath$\omega$ }}$. Illustrate the relative directions of the angular momentum ${\bf L}$ and the angular velocity $\hbox{{\boldmath$\omega$ }}$for cylinders with (a) $h< \sqrt{3} R$, (b) $h= \sqrt{3} R$, and (c) $h> \sqrt{3} R$.

[Hints can be found here, but do not follow this link until you have attempted the question on your own.]