# Angular momentum

## Homework Statement

A uniform solid disk of mass m = 4.50 kg and radius R = 25.0 cm rotates at 7.00 rad/s about
an axis perpendicular to the face of the disk. Calculate the magnitude of the angular momentum of the disk (a) when the axis of rotation passes through the center of the disk, and (b) when the axis of rotation is at the outer edge of the disk.

L = r x p
p = mv
v = rω

## The Attempt at a Solution

(a)
First I calculated v:

v = (.25)(7)
v = 1.75

I then calculated p:

p = (4.5)(1.75)
p = 7.875

I then calculated L:

L = (.25)(7.875)
L = 1.97

The answer I got for (a) is 1.97, however this is not correct. I am not sure what I am doing wrong. Any help would be greatly appreciated.

Thanks

## Answers and Replies

The formula you've given for angular momentum,
L=r x p
is valid only for a material point (pure, dimensionless mass).

You might want toread something about moment of inertia, and for B) try Steiner's theorem.

Ok thanks, I didn't realize L = r x p was only for that. I instead tried it with L = Iω and got .984 which is the correct answer.

For part (b), I don't think we ever learned about Steiner's theorem. I don't see it in my notes and it is not in the index of my textbook. Maybe I'm just missing something, but is there another way to solve (b)?

Well, you could integrate over the whole disc to get it's moment of inertia with respect to that axis, but I doubt you can do that, deffinitely not the high school level ;).

So give it a go and read about Steiner's theorem. Basically, it will allow you to calculate the moment of inertia with respect to an axis if you know the body's moment of inertia with respect to any other parallel axis. Apparently, in your exercise both axes ARE parallel.
To help you, according to steiner's theorem:
$$I=I_0+md^2$$, $$I_0$$ being the moment you know, m-mass of the body and d-distance between the axes.
What's the distance in your exercise?

Oh ok I actually see that equation in my notes, except it is marked as the parallel axis theorem, but I see that they are the same thing.

Well I used the equation to find 'I' for the edge of the disk and then used L = Iω and got the right answer!

Thanks a lot for all the help, it really makes a lot more sense to me now.