Question 4

A uniform brick of mass $M$ has the form of a cuboid with sides $a$, $b$ and $c$. Determine its principal moments of inertia for rotations about its centre.

[11 marks]

A brick with $b=a$ and $c=2a$ rotates about a space diagonal (passing through its centre and two of its corners) with constant angular velocity $\omega$. Find its angular momentum about its centre.

[8 marks]

Find the torque on the brick needed to maintain this rotation.

[6 marks]

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