Can Individual Zero Angular Momenta Result in Nonzero System Angular Momentum?

[jcruise322]

Homework Statement

Is it possible for the respective angular momenta of each individual particle in a system to be zero, but the system's collective angular momentum be nonzero?

For example, a puck on a frictionless air table moves (without spinning) toward a point on a rod that is not the center of mass of the rod, and orthogonal to the puck's direction of velocity. The puck strikes and sticks to the rod, causing the system to spin. The angular momentum of the puck and the rod is nonzero before the collision, but the angular momentum of the system after the collision is nonzero.

Homework Equations

L=Rxmv
L=I*W

The Attempt at a Solution

I thought that the angular momentum of a system was just the individual angular momenta of the components-it is true for linear momentum at least, but before the collision the angular momenta of the puck and rod are zero, after they are each non zero. Am I wrong? If I calculated the angular momenta of each particle in the system after the collision and made a summation, would I find it to be zero? Do we have to treat the particles in the system differently from the system itself? Appreciate any feedback, thanks!

 

[BvU]

angular momentum of the puck and the rod is nonzero before the collision

Nope. You have to take the axis of rotation into consideration too: angular momentum around the impact point is zero, but the system will rotate around some other point.

Not completely the same, but with the same idea is problem 1 (with solution) here.

 

[jcruise322]

Nope. You have to take the axis of rotation into consideration too: angular momentum around the impact point is zero, but the system will rotate around some other point.

?? Angular momentum around the impact point is nonzero. The system rotates around its center of mass. Both of them individually are zero in regard to angular momentum before the collision; they are non spinning.

 

[BvU]

?? Angular momentum around the impact point is nonzero

Before the collision it is zero. Stick lies still, puck $\vec r$ and $\vec p$ are along the same line.

 

[BvU]

puck on a frictionless air table moves (without spinning) toward a point on a rod that is not the center of mass of the rod, and orthogonal to the puck's direction of velocity

Perhaps we need a drawing: if the point on the rod is orhogonal to the puck's direction of velocity, there will be no collision ?

 

[jcruise322]

Before the collision it is zero. Stick lies still, puck $\vec r$ and $\vec p$ are along the same line.

Then that would mean angular momentum would not be conserved. I realize that the stick's angular momentum is zero and the puck has angular momentum RELATIVE to the stick. The only angular momentum is relative angular momentum of the system before the collision which can be quantified as rxmv for the puck before impact.

 

[jcruise322]

The puck is lying along the y-axis with its COM at the origin. The puck travels a distance above or below the y-axis in a straight horizontal line towards the rod

 

[BvU]

The puck is lying along the y-axis with its COM at the origin. The puck travels a distance above or below the y-axis in a straight horizontal line towards the rod

Now I really need a drawing