# If there was no friction would a thin rectangle with mass $m$ with sides $a$ and $b$ spin indefinitely about an axis through its diagonal?

I would like a geometrical physics answers so I can have an intuitive grasp about the problem. That means no nonphysical things like matrices, coordinates and random basis of vectors.

For example it the initial period of revolution was t , when is it going to stop.

• Do you mean the mass is a rectangle? Is the mass in free space, is one corner on a table? – jacob1729 May 28 at 9:16
• Look from energy point of view as the disappative forces don't exist so the energy of the system is a constant quantity and hence if the plate has a fixed moment of inertia then we have that it rotates for infinite time.... – Aditya Garg May 28 at 9:17
• Is there gravity or some other source of torque? If there is gravity, what is the orientation of the thin rectangle? – probably_someone May 28 at 10:00
• Gravity doesn't matter, if you had a square and it's rotating about a physical axis piercing it through it's diagonal it would never stop , but rectangle has a more complicated moment of inertia – Leo Kovacic May 28 at 12:33