Problem 1 -- Why don't the units work?

On problem 1 why don't the units work out?

For simplicity of the problem statement we've assumed that several constants (pendulum mass, length, and moment of inertia) are equal to 1. If you're interested in the full equations or their derivation, you can see them written out here: http://scienceworld.wolfram.com/physics/Pendulum.html