cultclassic
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2. A light, flexible, nonstretching cable is wrapped several times around a winch drum, a solid cylinder of mass 50kg and diameter 0.120m, which rotates about a stationary horizontal axis held by a frictionless bearing. The free end of the cable is pulled with a constant force of magnitude 9.0N for a distance of 2.0m. The cable unwinds without slipping, turning the cylinder as it does so. (a)Use the definition of the rotational inertia for a continuous body to show that the rotational inertia of the winch drum (or any solid cylinder) is I=1/2(MR^2), where M is the mass of the cylinder and R is its radius. [Let the mass element dm=?dV=?(2'pie'rLdr).]
You'll have to prove this by integration, it's probably in the textbook
b.)If the cyclinder is initally at rest, find its final angular speed and the final speed of the cable.
F = I x alpha (where alpha = angular acceleration)
calculate alpha from above:
final angular speed w = sqrt of (w0 + 2 x alpha x theta)
(where theta = angular displacement (see (d))
and
w0 = initial speed, which here is zero)
final speed of the cable = w x radius
C) Calculate the net torque (magnitude and direction) in the cylinder about its axis of roation.
Torque = Force x radius
for direction, use right-hand-rule
(d)What is the angular displacement of the cylinder as the cable is unwind?
angular displacement is how much the drum has rotated in degrees.
1 complete rotation => 360 degrees
ie: 2 x pi x R => 360 degrees
therefore the angle for 2.0 m => ((360) / (2 x pi x R) ) x 2.0
It bothers me that they've asked the question in the reverse order, ie: (d) should be first, because it's required for (a), so verify all this...
You'll have to prove this by integration, it's probably in the textbook
b.)If the cyclinder is initally at rest, find its final angular speed and the final speed of the cable.
F = I x alpha (where alpha = angular acceleration)
calculate alpha from above:
final angular speed w = sqrt of (w0 + 2 x alpha x theta)
(where theta = angular displacement (see (d))
and
w0 = initial speed, which here is zero)
final speed of the cable = w x radius
C) Calculate the net torque (magnitude and direction) in the cylinder about its axis of roation.
Torque = Force x radius
for direction, use right-hand-rule
(d)What is the angular displacement of the cylinder as the cable is unwind?
angular displacement is how much the drum has rotated in degrees.
1 complete rotation => 360 degrees
ie: 2 x pi x R => 360 degrees
therefore the angle for 2.0 m => ((360) / (2 x pi x R) ) x 2.0
It bothers me that they've asked the question in the reverse order, ie: (d) should be first, because it's required for (a), so verify all this...
Hubby piss you of or sunthin? Hating men right now?
I meant, verify my formulas above, because I may be wrong...
How about SanDisk or Kingston? These are the 2 names I keep on encountering on ebay, cheap too -- 10 bucks for 1, sometimes even 2 gigs. 
