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$ E_i = E_f $

$ \omega = \frac{v}{r} $

$ mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2 $

$ mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\frac{v^2}{r^2} $

$ 2gh = v^2 + \frac{Iv^2}{mr^2} $

$ 2gh = v^2(1 + \frac{I}{mr^2}) $

$ v = \sqrt{\frac{2gh}{1 + \frac{I}{mr^2}}} $

$ I = \frac{1}{2}mr^2 $

$ v = \sqrt{\frac{2gh}{1 + \frac{\frac{1}{2}mr^2}{mr^2}}} $

$ v = \sqrt{\frac{2gh}{1 + \frac{1}{2}}} $

$ v = \sqrt{\frac{4gh}{3}} $

$ g = 9.8 \frac{\mathrm{m}}{\mathrm{s}^2} $

$ h = .08 \mathrm{m} $

$ v = \sqrt{\frac{4*9.8 \frac{\mathrm{m}}{\mathrm{s}^2}*.08 \mathrm{m}}{3}} $

$ v = \sqrt{\frac{3.136\frac{\mathrm{m}^2}{\mathrm{s}^2}}{3}} $

$ v = \sqrt{1.045 \bar{3} \frac{\mathrm{m}^2}{\mathrm{s}^2}} $

$ v = 1.0224 \frac{\mathrm{m}}{\mathrm{s}} $

$ \theta = \frac{L}{2 \pi r} \mathrm{rev} $

$ \theta * \frac{2\pi}{1\mathrm{rev}} = \frac{L}{r} $

$ \theta = \frac{L}{r} = \frac{1}{2} \alpha t^2 $

$ \alpha = \frac{2L}{rt^2} $

$ \omega = \alpha t $

$ \omega = \frac{2L}{rt} $

$ v = \omega r $

$ v = \frac{2L}{t} $

$ L = .615 \mathrm{m} $

$ t = 1.1\bar{3} \mathrm{s} $

$ v = \frac{2*.615 \mathrm{m}}{1.1\bar{3} \mathrm{s}} $

$ v = 1.0853 \frac{\mathrm{m}}{\mathrm{s}} $

$ \frac{1.0853 \frac{\mathrm{m}}{\mathrm{s}} - 1.0224 \frac{\mathrm{m}}{\mathrm{s}}}{1.0224 \frac{\mathrm{m}}{\mathrm{s}}} = .0615 = 6.15% $