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January 29, 2015

January 29, 2015

Posted by **mariel** on Friday, December 3, 2010 at 2:41am.

- physics -
**drwls**, Friday, December 3, 2010 at 5:59amYou 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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