Posted by mariel on Friday, December 3, 2010 at 2:41am.
You will need to calculate the moment of inertia of the spool, which is
I = (1/2)M R^2 = (0.5)(0.5 kg)(.075m)^2
= 1.406*10^-3 kg m^2
The mass m on a string applies a torque of
T = m g R = 5*9.8*.075 = 3.675 N-m
(a) Angular acceleration of the spool is
(alpha) = T/I
Compute the number, in radians/s^2
(b) The angle rotated through when the string is fully unwound is
theta = L/(2 pi R)
The time t to unwind is given by
theta = (1/2)*(alpha)*T^2
Solve for T and then compute the angular velocity at that time:
w = alpha*T
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