Answer:
[tex]v = \sqrt{\frac{1.1g}{(1 + \frac{1}{r^2})}}[/tex]
Explanation:
By the law of energy conservation, the potential energy can be converted to kinetic energy and rotational energy as it rolling downhill
[tex]E_p = E_k + E_r[/tex]
[tex]mgh = 0.5mv^2 + 0.5m\omega^2[/tex]
Also velocity of the disk is its angular velocity times its radius:
[tex]gh = 0.5v^2 + \frac{v^2}{2r^2}[/tex]
[tex]gh = (\frac{v^2}{2})(1 + \frac{1}{r^2})[/tex]
[tex]v^2 = \frac{2gh}{(1 + \frac{1}{r^2}})[/tex]
[tex]v = \sqrt{\frac{2gh}{(1 + \frac{1}{r^2})}}[/tex]
[tex]v = \sqrt{\frac{1.1g}{(1 + \frac{1}{r^2})}}[/tex]
