(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle follows a trajectory given as R = Aθ, where θ is the polar angle.in a horizontal plane. The trajectory is such that the walls are vertical and the particle moves in a groove made by them. The particle remains in contact with both the walls throughout its motion. The side walls are smooth but the horizontal surface on which it moves is rough with coefficient of friction = μ. The particle was initially at R=A and given an initial velocity v_{o}in the direction of the trajectory at that point. Find:

(a) R as a function of time

(b) velocity of particle v as a function of time

(c) θ as a function of time

2. Relevant equations

general polar coordinate equations of motion

newtons laws

work energy theorem

3. The attempt at a solution

i tried to do the question by using polar coordinates. However I realised that the normal reaction was not in the direction of r(unit vector). and consequently, v(vec) was not in tangential direction. Then I tried to use work energy theorem as only friction was doing work. but that lead to an ugly integral. and further in that integral kmg.dr was quite ugly.

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# Motion in polar coordinates

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