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Standard XII

Physics

Moment of Inertia of a Disc

A small disc ...

Question

A small disc and a thin uniform rod of length $l$ , whose mass is $η$ times greater than the mass of the disc, lie on a smooth horizontal plane. The disc is set in motion, in horizontal direction and perpendicular to the rod, with velocity $v$ , after which is elastically collides with the end of the rod. Find the velocity of the disc and the angular velocity of the rod after the collision. At what value of $η$ will the velocity of the disc after the collision be equal to zero? Reverse its direction?

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Solution

A small disc and a disc uniform rod of length $= l$
Mass $= m η$
Mass of disc $= m$
Velocity $= v$
The attempt of the solution
Now, it is figured out that,
both linear and angular momentum and conserved here,
Conversing the angular momentum about the CM
$m v \frac{l}{2} = I ω + m v^{'} \frac{l}{2}$

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A small disc and a disc uniform rod of length=lMass=mηMass of disc=mVelocity =vThe attempt of the solutionNow, it is figured out that,both linear and angular momentum and conserved here,Conversing the angular momentum about the CMmvl2=Iω+mv′l2