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A uniform disc of radius R rolls perfect...

A uniform disc of radius `R` rolls perfectly over two horizontal plank `A` and `B` moving with velocities `v` and `2v`, respectively. Find the

a. velocity of `CM` of the disc.
b. angular velocity of the disc.

Text Solution

Verified by Experts

As the disc is rolling points `A` and `B` in which are on the disc and in contact with the planks will no slide. The velocities of points `A` and `B` should be the same as the planks. Let the disc rotate with an angular velocity `omega` and let the velocity of centre of the mass of the disc be `v_(c)`.

Velocity of point `A, v_(A),v_(c)+omegaR=v`...........i
Velocity of point `B, v_(B),omegaR-v_(c)=2v`..........ii
From eqn i and ii `omega=3v//R` and `v_(c)=-2v`
Hence velocity of centre of disc will be `2v` towards the left and the angular velocity will be `3v//R` the in the clockwise sense.
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