The answers are given. I need the mathmatical process to get the answer for ques

Question

The answers are given. I need the mathmatical process to get the answer for question 2. Question 1 is just M(R^2)/2.

You have a pulley11.1cm in diameter and with a mass of1.8kg. You get to wondering whether the pulley is uniform. That is, is the mass evenly distributed, or is it concentrated toward the center or the rim? To find out, you hang the pulley on a hook, wrap a string around it several times, and suspend your1.8kg physics book0.9m above the floor. With your stopwatch, you can find that it takes0.76s for your book to hit the floor.

1) What is the moment of inertia if the pulley is uniform?

ANSWER: 0.002772225

2) What is the actual moment of inertia of the pulley based on your measurement?

ANSWER: 0.01189124352

Explanation / Answer

1)The moment of inertia if the pulley is uniform

=> I = mr^2/2 (assuming it as a disk)
=> I = 27.7225 kg cm^2
=> I = 0.002772225 kg m^2


2)The actual moment of inertia of the pulley based on your measurement:

s = ut + 1/2 a*t^2
considering the book motion
=> 0.9 = 1/2 a*(0.76)^2
=> a = 3.116 m/s^2

=> angular acceleration of the pulley = a/r = 56.15 rad/s^2

=> I = / = F*r/a =

0.01189124352

kg m2

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