A drum of mass mA and radius a rotates freely with initial angular velocity W A,

Question

A drum of mass mA and radius a rotates freely with initial angular velocity W A, 0 A second drum with mass MB and radius b > a is mounted on the same axle and is at rest, although it is free to rotated. 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 and sticks to the outer drum. Find the subsequent angular velocities of the two drums WA and WB Ignore the transit time of the sand.

Explanation / Answer

the sand fly out but in the instant it fly out, it angular velocity is the same, so angular velocity of the larger drum is unchanged. Moment of inertia of the sand "disk". I=ms*a^2/2 -------------- so wb*(mb*b^2/2+I)=wa*I so wb=wa*I/(mb*b^2+I). where I=ms*a^2/2

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