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

a light string 4 meters long is wrapped around a solid cylindrical spool with a radius of 0.075 m and a mass of .5 kg.a 5kg mass is then attached to the end of the string, causing the string to unwind from the spool. a. what is the angular acceleration of the spool? b. how fast will the spool be rotating after all of the string has unwound?

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

- physics -
**chffvhcjf**, Wednesday, April 8, 2015 at 4:26pm
futzvuy

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