There's a metallic rod of length $l_1$ which is spinning around a vertical ax which passes through its center. The ends of the rod are spinning with $\omega_1$ angular speed. Determine the temperature at which to heat the metal rod so that the angular speed of the end $\omega_2$ doubles.
The only idea I have is the following: $\omega_1$ and $\omega_2$ are constant, so the net force is 0, and so the angular momentum $\vec{r} \times m\vec{v}$ is conserved. How should I approach this? And in general, for problems relating to torque or angular momentum, how should I approach those?
