# Angular speed problem

1. Apr 7, 2005

### coey

I'm kinda having trouble figuring out this problem...i already know that i have to use conservation of angular momentum Iiwi=Ifwf but i'm having trouble calculating the key part, the second moment of inertia. I'm pretty sure that im' supposed to be using this form of the calculation of inertia, I=Mr^2... but i still can't seem to solve it... like when i use it to test whether the numbers work out for the first moment of inertia 2.92 = 2.92*2 * 1.09^2, these numbers don't work out.

A student sits on a freely rotating stool holding two weights, each of mass 2.92 kg. When his arms are extended horizontally, the weights are 1.09 m from the axis of rotation and he rotates with an angular speed of 0.746 rad/s.

The moment of inertia of the student plus stool is 2.92 kg · m2 and is assumed to be constant. The student pulls the weights in horizontally to a position 0.307 m from the rotation axis.

Question: Find the new angular speed and find the kinetic energy before and after he pulls the weight inward.

2. Apr 7, 2005

### ZapperZ

Staff Emeritus
A number of issues here:

1. Never, EVER solve a physics problem by plugging in numbers at the very beginning. This is a big no-no and will create hell in your attempts at solving physics problems later on. Assign symbols to all the relevant quantities and solve the problem algebraically first. This also allows whoever is looking at your work to follow what you are doing clearer.

2. What is "The moment of inertia of the student plus stool is 2.92 kg · m2..."? m2? In any case, I will assume that I, the moment of inertia of the student+stool is known (at least to you).

3. There are TWO moment of inertias here: (i) moment of inertia of student+stool, which is I, which doesn't change, and (ii) moment of inertia of the two masses, which does change. Call it I1 and I2 for before and after.

Then your conservation equation should look like

(I+I1)w1 = (I+I2)w2

You want to solve for w2. You know I, you can calculate I1 and I2 (you were given the radius of revolution for each case), and you were given w1. Thus, w2 can be solved.

From this, the rotational KE should be baby algebra.

Zz.