Pendulum with angular velocity I have another pendulum problem again but this time it's with angular velocity. My question is: If a pendulum is initially at its unstable equilibrium position, then how large an initial angular velocity is necessary for the pendulum to go completely around? So basically we need to find a $\theta$ that will spin this pendulum around for 1 full period $T$. I am assuming `unstable equilibrium position` means that it is inverted therefore a slight push will send it out of the equilibrium position. I just don't understand how I would calculate something like that though.

If there is no friction, energy is conserved. Any velocity from the unstable equilibrium is enough to spin it all the way around.