Dynamics of Rotation; An Elementary Introduction to Rigid Dynamics

Cover Dynamics of Rotation; An Elementary Introduction to Rigid Dynamics
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— A oord, 8 feet long, is wrapped rov/nd the axle, 4 inches Ml dia/meter, of ahea/oy laheel, cmd is pulled with a constant force of 60 poimds till it is all wn/wound wnd comes off. The wheel is then found to be rotatmg 90 times a m/i/mde; find its moment of inertia.
Solution. — Using British absolute units. The unit of mass is 1 lb.
and of force 1 poundal.
The force of 60 pounds = 60 x 32 poundals. This is exerted through a distance of 8 feet ; .•, the work done by the force =8 x 60 x 32 ft. -p
...oundals.
(90 X SttX^ — 60~/' 28 Dynamics of Rotation.
Equating the two we have ilx9?r2=8x 60x32; . 1^2x8x60x32 n,.f^,^^t^_ 9jr2 It will be observed that this result is independent of the diameter of the axle round which the cord is wound, which is not involved in the solution. The torque exerted would indeed be greater if the axle were of greater diameter, but the cord would be unwound propor- tionately sooner, so that the angular^ velocity generated would remain the same.
TJsmg Engmeer's or gravitation units, the solution is as follows : — The unit of force is 1 pound and of mass 1 slug.


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