Question

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 `pi rad s^-1` and angular acceleration `pi//2 rad s^-2` and particle `B` moves with constant angular velocity `2 pi rad s^-2`. Find the time after which both the particlsd `A nad B` will collide.

Answer 1

Suppose the angle between `OA and OB = theta`. Then the rate of change of `theta`,
`theta = omega_B - omega_A = 2 pi - pi = pi rad s^-2`
`theta = prop_B - prop_A = (pi)/(2) rad s^-2`
If the angular displacement is `Delta theta`, then
`Delta theta = dot theta t + (1)/(2) ddot theta t^2`
For `A and B` to collide angular displacement, `Delta theta = pi`
`rArr pi = pi t + (1)/(2) ((-pi)/(2)) t^2 rArr t^2 - 4t + 4 = 0 rArr t = 2 s`.
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