Confused about direction in angular momentum

[DunWorry]

Homework Statement

Alright apologies I could not attach an image due to my inexperience of this but its simple to imagine.

Imagine a stick which can rotate about the centre of its axis, perpendicular to its length. I.e the ends can rotate freely in a clockwise, or anti clockwise manner. Now imagine a ball traveling right to left, and hits the top of the stick. At the same time, a ball traveling left to right hits the bottom of the stick. Let's say the balls have same mass and same velocity. The stick will rotate anti clockwise.

The balls will have equal and opposite LINEAR momentum, but do they have equal and opposite angular momentum relative to the rotational axis of the stick? angular momentum is L = r x mv = Iw. For an object traveling in linear motion relative to some origin to find the angular momentum we use L = r x mV. I thought mV was just its linear momentum, so it should be opposite, but then again both the balls are helping the stick rotate in the same direction, so does that mean they have the same direction in terms of angular momentum?

 

[MrWarlock616]

Angular momentum is same at every point in the orbit.

 

[Doc Al]

For an object traveling in linear motion relative to some origin to find the angular momentum we use L = r x mV.

Right.

I thought mV was just its linear momentum, so it should be opposite, but then again both the balls are helping the stick rotate in the same direction, so does that mean they have the same direction in terms of angular momentum?

Yes. Actually figure out the direction of the angular momentum for each ball using the right hand rule for cross products. You'll find that the angular momentum of each ball points in the same direction.

 

[gneill]

You can use the right-hand-rule to determine the direction of the result of the cross products r x v. If the directions for both are the same, then their angular momenta will also point in the same direction.

Edit: Doh! Doc Al got there ahead of me!

 

[DunWorry]

Ahhhhh, TRUE I didnt think of the right hand rule. So am I correct in thinking that two linearly moving objects can have opposite linear momentum but same angular momentum?

 

[MrWarlock616]

Yes!