# Problem with formula for cylindrical chandelier problem

The problem says:

A cylindrical chandelier is hung on a wire and when it rotates around its siege an angle $$\theta$$ the twisting moment acting on it is $$\tau$$ = $$−\theta$$. The moment of inertia is unitary and its angular velocity in the equilibrium position is unitary. Calculate the maximum twist angle $$\theta_0$$, ...

And the suggested solution is:

From the conservation of mechanical energy: $$\frac{1}{2} = \frac{1}{2}\theta_0^2$$ so $$\theta_0 = 1$$

But where does this formula came from?

• It would be more accurate to say "From the work energy theorem" instead of "conservation of mechanical energy". You can find the KE at $\theta =0$ and $\theta = \theta_0$, and the work done by the twisting moment. Jun 30 '20 at 10:29

The chandelier is in an SHM since $$\tau=-\theta$$, where $$\kappa=1$$. Since the kinetic energy in the equilibrium position equals the potential energy at the amplitude position, $$\frac12I\omega^2=\frac12\kappa\theta_0^2$$.
• Then why $I \omega^2 = 1$? Jun 30 '20 at 10:49
• It is given that $I=1$kgm$^2$ and $\omega=1$rad/s at the equilibrium position. Jun 30 '20 at 10:52