sorry about the added m into the term for rotational kinetic energy, it's a typo.
as of the moment of inertia I=1/3mL2, assuming m is the mass, L is the length of the object, so the new equation is:
mgh=mgh(1-sinθ)+0.5Iω2, I=1/3mL2
mgh=mgh(1-sinθ)+(1/2)(1/3)m(2h)2ω2, ω=θ/t...