Solve Mass Homework w/ Pullys: Is it Uniform?

[viciousp]

Homework Statement

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

Homework Equations

t= r x F
t = I$$\alpha$$
F= ma

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?

 

[rl.bhat]

Your calculation is correct.

 

[kerimek]

I would say that your approach and calculations are correct. Based on your calculations, the moment of inertia for the pulley is not equal to the moment of inertia for a uniform disk of the same mass and radius. This suggests that the pulley is not uniform. However, to confirm this conclusion, it would be beneficial to repeat the experiment with different masses and distances to ensure accuracy and consistency in the results. Additionally, checking for any other factors that may affect the results, such as friction or air resistance, would also be important. Overall, your approach and conclusion are valid, but further experimentation and analysis may be needed for a more conclusive answer.