A rope of uniform linear density p and mass m is wrapped one complete turn around a hollow cylinder of mass M and radius R. The cylinder rotates freely about its axis as the rope unwraps (Figure 9-9). The rope ends are at x = 0 (one fixed, one loose) when point Pis at 0 0, and the system is slightly dis- placed from equilibrium at rest. Find the angular velocity as a function of angular displacement of the cylinder. -
A rope of uniform linear density p and mass m is wrapped one complete turn around a hollow cylinder of mass M and radius R. The cylinder rotates freely about its axis as the rope unwraps (Figure 9-9). The rope ends are at x = 0 (one fixed, one loose) when point Pis at 0 0, and the system is slightly dis- placed from equilibrium at rest. Find the angular velocity as a function of angular displacement of the cylinder. -
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Transcribed Image Text:A rope of uniform linear density p and mass m is wrapped one complete turn
around a hollow cylinder of mass M and radius R. The cylinder rotates freely
about its axis as the rope unwraps (Figure 9-9). The rope ends are at x = 0
(one fixed, one loose) when point Pis at 0 = 0, and the system is slightly dis-
placed from equilibrium at rest. Find the angular velocity as a function of
angular displacement of the cylinder.
-
P
(a)
Rotation
➜+
dx
X
O
R
(b)
dx
R sin p
= 12
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