A drum of mass Ma and radius a rotates freely with initial angular velocity ωa0. 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 holes in the inner drum are opened. The sand starts to fly out at a constant rate λ = dm/dt and sticks to the outer drum. (a) Explain, in detail, why the angular velocity of the inner drum will remain constant. (b) Determine the angular velocity of the outer drum ωb(t). Ignore the transit time of the sand
A drum of mass Ma and radius a rotates freely with initial angular velocity ωa0. 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 holes in the inner drum are opened. The sand starts to fly out at a constant rate λ = dm/dt and sticks to the outer drum. (a) Explain, in detail, why the angular velocity of the inner drum will remain constant. (b) Determine the angular velocity of the outer drum ωb(t). Ignore the transit time of the sand
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
A drum of mass Ma and radius a rotates freely with
initial angular velocity ωa0. 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 holes in the inner drum
are opened. The sand starts to fly out at a constant rate λ = dm/dt
and sticks to the outer drum. (a) Explain, in detail, why the angular
velocity of the inner drum will remain constant. (b) Determine the
angular velocity of the outer drum ωb(t). Ignore the transit time of
the sand
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