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Two particles A and B move on a circle. Initially particles A and B are diagonally opposite to each other. Particle A moves with angular velocity πrads1 and angular acceleration π/2rads2 and particle B move with constant angular velocity 2πrads2. Find the time after which both the particles A and B will collide.

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Solution

Suppose the angle between OA and OB = θ. Then the rate of change of θ,
θ=ωBωA=2ππ=πrads2
θ=αBαA=π2rads2
If the angular displacement is Δθ, then
Δθ=˙θt+12¨θt2
For A and B to collide angular displacement,
Δθ=π.
π=πt+12(π2)t2t24t+4=0t=2s

1006882_983418_ans_6ce7c6dc194f43869fa8f0586c242e10.PNG

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