Question 2

A uniform rectangular plate has sides of length $a$ and $2a$. It is free to rotate about one of its corners, which is held fixed. Calculate its moment of inertia tensor about this corner.

The plate rotates with angular velocity $\omega$ about the diagonal through this corner.

(a) Find the corresponding (vector) angular momentum of the plate.

(b) Find the rotational kinetic energy of the plate.

(c) What torque must be exerted about the corner of the plate in order to maintain this rotation?

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