Two horizontal turntables are in contact with each other at their outer edges, a

Question

Two horizontal turntables are in contact with each other at their outer edges, and the static friction between them allows them to turn together (in opposite directions) without slipping. The larger turntable has a radius of 0.36m, and the smaller turntable a radius of 0.12m. The larger turntable accelerates from rest at a rate of 1.5rad/s^2, and just when it completes its third revolution, a ball of clay that was (until now) stuck to the outer edge of the smaller turntable flies off. Find the speed of the ball of clay as it leaves the turntable

Explanation / Answer

here,

radius of the larger turntable , rl = 0.36 m

radius of the smaller turntable , rs = 0.12 m

accelration , alphal = 1.5 rad/s^2

let the angular accelration of smaller be alphas

as the tangential accelration for both the table is same

alphal * rl = alphas * rs

1.5 * 0.36 = alphas * 0.12

alphas = 4.5 rad/s^2

angle travelled , theta = 6 pi

let the final speed be w

w = sqrt(2 * alphas * theta)

w = sqrt( 2 * 4.5 * 6 *pi)

w = 13.02 rad/s

the speed of the clay when it leaves the turntable , v = rs * w

v = 1.56 m/s

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