# Conservation of angular momentum during collisions

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• anon90
In summary, during collisions between objects, if the net external force is zero, the linear momentum is conserved. However, even when the system is not isolated, the linear momentum can still be considered conserved if the external forces are not impulsive. This also applies to the pivot point chosen for angular momentum conservation, as long as the net external torque is zero. Non-impulsive forces can be ignored for the conservation of angular momentum during collisions, just like for linear momentum.

#### anon90

Hello everyone, I have a doubt regarding the conservation of angular momentum.
When dealing with collisions between two objects, if the net external force is zero we know that the linear momentum is conserved; even when the system is not isolated, for instance because of gravity acting on the said bodies, if the external forces are not impulsive (such as gravity force) we can neglect them, as their impulse over the small interval of the collision is small. So, while the linear momentum is theoretically not conserved, for all purposes it is.

Now, if we consider a rigid rod AB, hinged at point A, initially at rest in the vertical position, that can rotate around a horizontal axis passing on A, and we shoot a small bullet at the other extreme B, with a velocity perpendicular to the rod AB, the linear momentum is not conserved, as there will be an impulsive force on A keeping the rod fixed at that point.
That being said, if we choose A as the pivot the net external torque wrt that point is zero, and angular momentum is conserved.
Although this was a special case, since the torque due to the weight of both the bullet and the rod was zero because the rod starts in a vertical position, and the weights have the same direction... what if that is not the case?

My question is the following: if we have a system, and during a similar collision the next external torque is not zero, if the forces causing said torques are not impulsive, can we ignore them, and consider only the external torque due to the impulsive ones?
For instance if we have the rod on a horizontal plane and we shoot the bullet with a velocity perpendicular to it, but this time the weight of said bullet has a non zero torque wrt the hinge; the torque due to the weight of the rod is balanced with the torque due to the normal, if we assume the rod to be laying on a table.
My answer would be that yes, we can neglect them, since the angular impulse deriving from non impulsive forces will be close to zero when considering a small interval. So, again, we can say that the angular momentum will be approximately conserved wrt that specific pivot during the collisions if we choose to ignore, for instance, the torque due to gravity.

My doubt arises because in the books I've read so far (not English ones, so the titles won't matter) they always specify that you can ignore non impulsive forces for the linear momentum's conservation, but when talking about the angular momentum's, they never say so.
I've also noticed some videos online that treats such cases always ignore the torque due to non impulsive forces, without specifying why they do so.

anon90 said:
For instance if we have the rod on a horizontal plane and we shoot the bullet with a velocity perpendicular to it, but this time the weight of said bullet has a non zero torque wrt the hinge; the torque due to the weight of the rod is balanced with the torque due to the normal, if we assume the rod to be laying on a table.
My answer would be that yes, we can neglect them, since the angular impulse deriving from non impulsive forces will be close to zero when considering a small interval. So, again, we can say that the angular momentum will be approximately conserved wrt that specific pivot during the collisions if we choose to ignore, for instance, the torque due to gravity.
You have completely lost me with the description of this scenario.

I think that we have a rod which is connected to a horizontal hinge on one end. It is lying on a table so that it does not swing down to the vertical.

We fire a bullet vertically at the rod from from above. And for some reason we consider that the supporting force from the table does not become impulsive?!

The support force from the table most certainly will become impulsive in such a case. It is a constraint force. It will take on whatever value (including near-infinite impulsive values) is required to maintain the constraint.

jbriggs444 said:
You have completely lost me with the description of this scenario.

I think that we have a rod which is connected to a horizontal hinge on one end. It is lying on a table so that it does not swing down to the vertical.

We fire a bullet vertically at the rod from from above. And for some reason we consider that the supporting force from the table does not become impulsive?!

The support force from the table most certainly will become impulsive in such a case. It is a constraint force. It will take on whatever value (including near-infinite impulsive values) is required to maintain the constraint.
I'm sorry that the description was that confusing, I've looked for some pictures online that may describe my situation and I've found the attached one.
Basically, instead of having a hanging rod, said rod is laying on a horizontal plane, and then we hit one extreme with a flying bullet.
During the collision the hinge will exert an impulsive force for sure, since that's why the rod is not moving away, but its torque wrt the hinge will be zero. The torque due to the weight and the normal force will balance each other, and either way they're not aligned with the axis of rotation.
My doubt was regarding to the torque due to the weight of the flying bullet, just before the collision: granted, it is once again not aligned with the axis of rotation, and since the rod cannot swing down to the vertical, so now that I think about it again I'm not even sure why I am considering it at all.

This bad example aside though, my question was whether one can, in general, neglect the torque of non impulsive forces during a collision in order to conserve the angular momentum, the same way we neglect non impulsive forces for linear momentum.

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anon90 said:
my question was whether one can, in general, neglect the torque of non impulsive forces during a collision in order to conserve the angular momentum, the same way we neglect non impulsive forces for linear momentum.
Yes, we can neglect non-impulsive forces for the duration of a brief collision, regardless of whether we are considering their effect on linear momentum or on angular momentum.

## 1. What is conservation of angular momentum during collisions?

The law of conservation of angular momentum states that the total angular momentum of a system remains constant in the absence of external torques. This means that during a collision, the total angular momentum of the system before the collision is equal to the total angular momentum after the collision.

## 2. Why is conservation of angular momentum important in collisions?

Conservation of angular momentum is important in collisions because it helps us understand and predict the behavior of objects during a collision. It allows us to analyze the changes in velocity and direction of objects involved in the collision.

## 3. How is angular momentum calculated during a collision?

The formula for calculating angular momentum during a collision is L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. The moment of inertia is the measure of an object's resistance to rotational motion and can be calculated using the mass and shape of the object.

## 4. Does conservation of angular momentum apply to all types of collisions?

Yes, conservation of angular momentum is a fundamental law of physics and applies to all types of collisions, including elastic and inelastic collisions. However, inelastic collisions involve some energy loss and therefore, the total angular momentum may not be conserved.

## 5. How does conservation of angular momentum apply to real-world collisions?

In real-world collisions, conservation of angular momentum is always observed, but it may not be the only factor that affects the outcome of the collision. Other factors such as friction, air resistance, and external forces may also play a role. However, the principle of conservation of angular momentum still holds true in all collisions.