Angular momentum in a particle system

[Shadow Cloud]

Figure 11-26 shows three particles of the same mass and the same constant speed moving as indicated by the velocity vectors. Points a, b, c, and d form a square, with point e at the center. Rank the points according to the magnitude of the net angular momentum of the three-particle system when measured about the points, greatest first (use only the symbols > or =, for example a>b>c=d=e).

http://files.upl.silentwhisper.net/upload5/phyprob.GIF


Okay, so angular momentum is equal to mass (radius cross product velocity). Since velocity is constant and the mass is the same, this leads only the radius or distance to compare. However, I am not quite sure how I should judge the distance of the particles. I mean what is the origin or the reference point that should use to judge these particles from?

 

[Astronuc]

Perhaps label each ball with 1, 2, 3 and decide which balls contribute the angular momentum with respect to each point, a, b, c, d, e.

 

[quicknote]

In this case, I would assume that the origin is the center of the square (point e).

In that case, the angular momentum would be highest at point e, since it is the farthest from the center and has the largest radius. Therefore, the ranking would be e > a > b = c > d. This is because a, b, c, and d all have the same distance from the center, but a has a slightly larger radius than b, c, and d. So, the final ranking would be e > a > b = c > d.