# Confused about direction in angular momentum

• DunWorry
In summary, the conversation discusses the concept of angular momentum in relation to two balls hitting a rotating stick. It is determined that although the balls have equal and opposite linear momentum, they also have equal and same direction angular momentum due to the right-hand rule for cross products. Therefore, it is possible for two linearly moving objects to have opposite linear momentum but the same 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?

Angular momentum is same at every point in the orbit.

DunWorry said:
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.

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!

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?

Yes!

## 1. What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of an object. It is defined as the product of an object's moment of inertia and its angular velocity.

## 2. How is angular momentum different from linear momentum?

Linear momentum is a measure of an object's motion in a straight line, while angular momentum is a measure of an object's rotational motion around an axis. They are both conserved quantities, meaning they remain constant in the absence of external forces.

## 3. Can angular momentum change?

Yes, angular momentum can change if there is a net torque acting on the object. This can be caused by external forces or by changes in the distribution of mass within the object.

## 4. What is the conservation of angular momentum?

The conservation of angular momentum states that the total angular momentum of a system remains constant as long as there is no external torque acting on the system. This means that if one object in the system gains angular momentum, another object must lose an equal amount of angular momentum.

## 5. How does angular momentum affect the motion of objects?

Angular momentum plays a crucial role in the motion of objects, especially those that rotate. It determines how fast an object will rotate, how much torque is needed to change its rotation, and how stable its rotational motion will be. In many cases, the conservation of angular momentum can help us predict the behavior of rotating objects.

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