# Conservation of angular momentum of a bullet

• refrigerator
The bullet's total conservation of momentum then says that the angular momentum of the bullet must be less than the angular momentum of the rod.

#### refrigerator

I was thinking of a couple basic mechanics problems lately. What if you have a rod sitting in space at rest, and you shoot a bullet at its center. Linear momentum is conserved, and the problem is quite trivial.

Now what if the bullet hit the rod slightly off of the rod's CG? I think linear momentum is conserved so the CG velocity of the rod is the same as with the problem above. However, I think the rod should also rotate.

So my question is, is angular momentum conserved here? Initially it seems the rod and bullet have purely linear motion, so no angular momentum, but after collision there clearly would be angular momentum.

I have thought about this but can't seem to figure out where the error in my reasoning is. Can somebody show me what's going on, or at least try to give me a fresh perspective?

Refrigerator

Even a point mass can have angular momentum. Suppose you fire that bullet horizontally from a gun while standing upright. That bullet has non-zero angular momentum from the perspective of a reference frame with its origin at your feet.

When you are looking at angular momentum, you have to look at the total angular momentum of the system, not just that of spinning things like your rod.

• 1 person
The bullet has orbital angular momentum even though it has no spin angular momentum

Angular momentum is always conserved but it has a different value depending on where you put the origin. Even if the bullet is moving in a straight line, it still has angular momentum measured relative to a point that is displaced from the path of the bullet.

Usually you want to do this problem in the center of mass frame. If the bullet is hitting the end of the rod, the bullet flies some distance from the center of mass.

## 1. What is conservation of angular momentum of a bullet?

The conservation of angular momentum of a bullet is a principle in physics that states that the total angular momentum of a system remains constant in the absence of external torque. This means that the angular momentum of a bullet will remain the same throughout its trajectory, as long as there are no external forces acting on it.

## 2. How does conservation of angular momentum affect the trajectory of a bullet?

The conservation of angular momentum plays a crucial role in determining the trajectory of a bullet. As the bullet is released from the barrel of a gun, it has a certain amount of angular momentum due to its spin. This angular momentum remains constant as the bullet travels through the air, causing it to follow a curved path due to the Earth's rotation.

## 3. What factors can affect the conservation of angular momentum of a bullet?

The conservation of angular momentum of a bullet can be affected by external forces such as air resistance, wind, and gravitational forces. These forces can cause the bullet to deviate from its original trajectory and reduce its angular momentum.

## 4. How is the conservation of angular momentum of a bullet related to its stability?

The conservation of angular momentum is closely related to the stability of a bullet in flight. A bullet with a higher angular momentum will be more stable and less affected by external forces, resulting in a more accurate and consistent trajectory.

## 5. Can the conservation of angular momentum of a bullet be violated?

No, the conservation of angular momentum is a fundamental principle in physics and cannot be violated. However, external forces can cause changes in the bullet's trajectory and affect its angular momentum, making it appear as if the conservation law is being violated.