# Dyanmics of Rotational Motion

1. Dec 2, 2007

### rwx1606

1. The problem statement, all variables and given/known data
I'm stuck on two problems so I'll just write them both here.
A. A 2.00kg textbook rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.150m, to a hanging book with mass 3.00kg. The system is released from rest, and the books are observed to move 1.20m in .800s. What is the tension in each part of the cord. What is the moment of inertia of the pulley about its rotational axis.
B.Two weights are connected by a very light flexible cord that passes over a 50.0N frictionless pulley of radius .300m. The pulley is a solid uniform disk and is supported by a hook connected to the ceiling. What force does the hook exert on the hook. The weight on the left is 75.0N, and the weight on the right is 125N.

2. Relevant equations
A.τ = Iα, I=1/2MR^2,$$\alpha$$=a/R

B.I=1/2MR^2

3. The attempt at a solution
A. For this problem I used Newton's 2nd Law for the two books to calculate the tension. The horizontal tension, which I'll call T1, was equal to 2a. The vertical tension, T2, is a mg+ma=29.4+3a. I then proceeded to calculate the net torque and got a (T1-T2)R. And set that equal to the moment of inertia I, times the angular acceleration. I converted the angular acceleration into terms of translational acceleration. So (T1-T2)R=1/2MR^2(a/R). After eliminate some variables, I get that the a=2(T1-T2)/M. The trouble is, I have three sets of equations to solve for the tensions, and acceleration but how do I get M, the mass of the pulley?
B.I don't get the concept in this question. I attempted to just add the weight of the pulley and the two weights and this was equal to 250N. I know the ceiling will pull up on the hook with the same force the pulley pulls down on the hook with. But the answer is 239N and I don't know how they got that. I know I'm missing something key, but can't quite figure it out.

Any help is appreciated! Thank you for taking the time to read.

2. Dec 3, 2007

no one? :(

3. Dec 3, 2007

### hage567

For the first question, you were given enough information in the question to find 'a' without having to solve for it with your system of equations. Figure out that, and things should become easier.

For the second question, I think the masses are supposed to be moving. So how would that change things?