A uniform, hollow, cylindrical spool has inside radius R/2, outside radius R, and mass M(Fig. P10.47). It is mounted so that it rotates on a fixed, horizontal axle. A counterweight of mass m is connected to the end of a string wound around the spool. The counterweight falls from rest at t= 0 to a position y at time t. Show that the torque due to the friction forces between spool and axle is 7 = R [m (8 – # ) – M ] Figure P10.47 м R/2 R/2

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Chapter1: Units, Trigonometry. And Vectors
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A uniform, hollow, cylindrical spool has inside radius R/2, outside
radius R, and mass M (Fig. P10.47). It is mounted so that it rotates
on a fixed, horizontal axle. A counterweight of mass m is
connected to the end of a string wound around the spool. The
counterweight falls from rest at t= 0 to a position y at time t. Show
that the torque due to the friction forces between spool and axle is
y = R |m (8 -) - M|
m(g
412
Figure P10.47
M
R/2
R/2
Transcribed Image Text:A uniform, hollow, cylindrical spool has inside radius R/2, outside radius R, and mass M (Fig. P10.47). It is mounted so that it rotates on a fixed, horizontal axle. A counterweight of mass m is connected to the end of a string wound around the spool. The counterweight falls from rest at t= 0 to a position y at time t. Show that the torque due to the friction forces between spool and axle is y = R |m (8 -) - M| m(g 412 Figure P10.47 M R/2 R/2
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