A stick of mass density $\rho$ per unit length rests on a circle of radius $R$ which makes an angle $\theta$ with horizontal and tangent to the circle at its upper end. Find the friction between them?

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written 9.5 years ago by

anjij • 70

modified 3.8 years ago by

pedsangini276 • 4.8k

Indian Institute of Science Education and Research > Physics > Sem 2 > Classical Mechanics

Marks : 20M

Year : April 2015

engineering physics

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written 9.5 years ago by

anjij • 70

Let $N$ be the normal force between stick and circle and let $F_f$ be the friction between ground and circle (see figure below). Then we immadiatly see that the friction force between stick and circle is also $F_f$, because the torques from the two friction forces on the circle must …

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That circle isn't in horiz equilibrium because Nsin@, Fcos@ and F all point to the left.

N (on the circle) points to the circle's centre, equal & opposite to N (on the stick). F (on the circle) is equal & opposite to F (on the stick).

Note the 'N' in your diagram is infact N (on the stick), which was used in taking moments.

Also tan@ doesn't equal sin@/(1 + cos@), this re-arranges to tan@ + sin@ = sin@, which is wrong. Its tan(@/2) = sin@/(1 + cos@).

8.4 years ago by nima.alyson • 0

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