Angular momentum of a particle system

[jhu2011]

Homework Statement

Calculate the total angular momentum of the system of particles pictured in Figure P.10 about the origin at 0. Figure is at www.webassign.net/reese1/p10-10.gif.

Homework Equations

L = r X p

p = mv

The Attempt at a Solution

Since you are taking a vector product, there is no i or j component to the angular momentum, meaning there will just be k perpendicular to the plane. I read somewhere that when doing a system of particles, you should take the angular momentum of each separate particle and then add it up. However, when I do this I don't get the right answer... Using L = r X p:

For 1st 3m: -4i + 2j X -3i = 6k
For 1st 2m: 1i + 2j X 2i = -4k
For 2nd 2m: 1i -2j X 2j = 2k

And 6 - 4 + 2 = 4k, which is NOT the right answer. I don't know what I've done wrong...

 

[LowlyPion]

Homework Statement

Calculate the total angular momentum of the system of particles pictured in Figure P.10 about the origin at 0. Figure is at www.webassign.net/reese1/p10-10.gif.

Homework Equations

L = r X p
p = mv

The Attempt at a Solution

Since you are taking a vector product, there is no i or j component to the angular momentum, meaning there will just be k perpendicular to the plane. I read somewhere that when doing a system of particles, you should take the angular momentum of each separate particle and then add it up. However, when I do this I don't get the right answer... Using L = r X p:

For 1st 3m: -4i + 2j X -3i = 6k
For 1st 2m: 1i + 2j X 2i = -4k
For 2nd 2m: 1i -2j X 2j = 2k

And 6 - 4 + 2 = 4k, which is NOT the right answer. I don't know what I've done wrong...

Welcome to PF.

Your 3rd r vector should be <1.2i, -2j> shouldn't it?

 

[jhu2011]

Welcome to PF.

Your 3rd r vector should be <1.2i, -2j> shouldn't it?

Indeed it should be. That 1.20 is so close to the 1.00! I got the correct answer now. Thanks a lot!