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Question Number 54462 by ajfour last updated on 03/Feb/19

Commented by ajfour last updated on 04/Feb/19

$$Findnecessary{\omega }_{0}thatneedbe$$$$giventothespheresuchthatit$$$$reachestheverticalwall,rolling$$$$purelyalongtheincline.$$

Answered by mr W last updated on 04/Feb/19

$$[b\tan \alpha +R\tan (\frac{\pi }{4}-\frac{\alpha }{2})-R]mg=\frac{1}{2}\times (\frac{2{mR}^2}{5}+{mR}^2){\omega }_0^2$$$$[\frac{b}{R}\tan \alpha +\tan (\frac{\pi }{4}-\frac{\alpha }{2})-1]g=\frac{7R}{10}{\omega }_0^2$$$$\Rightarrow {\omega }_0=\sqrt{\frac{10g}{7R}[\frac{b}{R}\tan \alpha -\frac{2\tan \frac{\alpha }{2}}{1+\tan \frac{\alpha }{2}}]}$$

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