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Slickepot
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Homework Statement
A drum of mass MA and radius a rotates freely with initial angular velocity ωA(0). A second drum with mass MB and radius b > a is mounted on the same axis and is at rest, although it is free to rotate. A thin layer of sand with mass Ms is distributed on the inner surface of the smaller drum. At t=0, small perforations in the inner drum are opened. The sand starts to fly out at a constant rate λ and sticks to the outer drum. Find the subsequent angular velocities of the two drums ωA and ωB. Ignore the transit time of the sand.
(picture available if needed)
Homework Equations
Angular momentum L=Iω
I for these drums , I=R2Mω
The Attempt at a Solution
At t=0, L(0)=a2(MA+MS)ωA(0).
and at L(t) = a2(MA+MS-λt)ωA+b2(MB+λt)ωB
conservation of angular momentum for the system, L(0)=L(t).
and put λt=MB and b=2a (because of answer hint).
I arrive at,
(MA+MS)(ωA(0)-ωA)+MBωA=8MBωB
and answer to this hint is ωB=ωA(0)/8
which I would get if ωA(0)-ωA = 0
Any suggestions what I'm missing?
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