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

- math -
**Saira**, Tuesday, November 17, 2015 at 12:15pm
A spool has a radius of 5cm . A string is 8.8 m long. How many times can the string be wound around the spool?

## Answer This Question

## Related Questions

- Physics - A string is wound around a solid cylindrical spool of mass 9.7 kg and ...
- Physics - Use conservation of energy to determine the angular speed of the spool...
- physcs - A string is wrapped around a uniform solid cylinder of radius 3.10 cm, ...
- physics - A 4.00-m length of light nylon cord is wound around a uniform ...
- Physics - Red ribbon wound around a red spool (above) is taped to blue ribbon ...
- phy - Review. An object with a mass of m 5 5.10 kg is attached to the free end ...
- Physichs - Two metal disks, one with radius R1 = 2.40 cm and mass M1 = 0.900 kg ...
- physics - A string is wrapped around a uniform disk of mass M = 1.6 kg and ...
- Physics - A 90kg stuntman falls from a building that is 80 meters tall. (Vo = 0)...
- physics - A 90kg stuntman falls from a building that is 80 meters tall. (Vo = 0...

More Related Questions