\begin{aligned}x & = R θ \\ v & = R ω \\ a & = R α \end{aligned}

α = \frac{τ}{I}

α = \frac{R(Mg) sin(θ)}{\frac{2}{5}MR^{2}}

Rot KE = \frac{1}{2}Iω^{2}

Rot KE_{f} = Rot KE_{i} + Work_{net}
Rot KE_{f} = Rot KE_{i} + ∫ τ⃗ · d⃗θ

α = \frac{R(Mg) sin(θ)}{\frac{5}{3}MR^{2}} = \frac{3}{5} \frac{g sin(θ)}{R}

a = α R = \frac{3}{5} g sin(θ)

v_{f}^{2} = v_{i}^{2} + 2aL = 0 + 2 \frac{3}{5} g sin(θ) L = \frac{6}{5} g h

v_{f} = \sqrt{\frac{6}{5}gh}

L = \frac{1}{2} at^{2} = \frac{1}{2} \frac{3}{5} g sin(θ) t^{2} = \frac{3}{10} g sin(θ) t^{2}

L = \frac{3}{10} g (\frac{h}{L}) t^{2}

t = \sqrt{\frac{\frac{10}{3}L^{2}}{gh}}