# Pullys with a mass

1. Dec 4, 2009

### viciousp

1. The problem statement, all variables and given/known data
You've been given a pulley for your birthday. It is a fairly big pulley 12 cm in diameter and with mass 2kg. You get to wondering if the pulley is uniform. To find out, you hang a 1kg textbook 1.0 meters above the floor and use a stopwatch to measure the time it takes it to fall (.71 seconds). What can you conclude about the pully

2. Relevant equations
t= r x F
t = I$$\alpha$$
F= ma

3. The attempt at a solution

I solved for the acceleration of the books

1.0 = .5a(.71)^2
a= 3.97 m/s^s

Then used force equation on the book with a mg down and T up (axises are pointing down and to the right)

mg- T = ma
T= m(g-a) = 5.83N

Since the tension is equal to the force of on the pully I used it to find the torque on the pully

t= r x F
t=(.06)(5.83) = .350 N*m

I used to the torque to solve for Moment of Inertia using the other torque equation

t= I( a/r)
t(r/a)= I = .0053 kg*m^2

Then I solved for Moment of Inertia of a uniform disk
I= 1/2Mr^2
I=.5(2)(.06)^2 = .0036 kg * m^2

Since the two moments on inertia are not the same the pully is not uniform. Is that correct?

2. Dec 4, 2009

### rl.bhat

Your calculation is correct.

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