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Question Number 109540 by ajfour last updated on 24/Aug/20

Commented by ajfour last updated on 24/Aug/20

$$Ifupperrodstartsturningwhen$$$$\theta =0,findNormalreactionfrom$$$$groundasafunctionofangle\theta .$$$$Neglectfriction.$$

Answered by mr W last updated on 25/Aug/20

$$mg\frac{l\sin \theta }{2}=\frac{{ml}^2}{3}\alpha$$$$\Rightarrow \alpha =\frac{3g\sin \theta }{2l}$$$$\Rightarrow \omega \frac{d\omega }{d\theta }=\frac{3g\sin \theta }{2l}$$$$\Rightarrow \frac{{\omega }^2}{2}=\frac{3g(1-\cos \theta )}{2l}$$$$\Rightarrow {\omega }^2=\frac{3g(1-\cos \theta )}{l}$$$$mg+mg-N=m\frac{l\alpha }{2}\sin \theta +\frac{l}{2}m{\omega }^2\cos \theta$$$$2mg-N=\frac{3mg{\sin }^2\theta }{4}+\frac{mg(6\cos \theta -6{\cos }^2\theta )}{4}$$$$\Rightarrow N=mg[2-\frac{3(1-\cos \theta )(1+3\cos \theta )}{4}]$$

Commented by mr W last updated on 24/Aug/20

Commented by ajfour last updated on 25/Aug/20

$$\mathcal{T}hisseemsentirelyalrightnow,$$$$thanksalotSir!$$

Commented by mr W last updated on 25/Aug/20

$$thanks!$$

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