# Conservation of Momentum (Linear and Angular)

• Felix83
In summary, the conservation of linear momentum can be used to find the final speed of the center of mass of a system after a collision. To find the angular speed of the bar/clay system rotating about its center of mass, conservation of angular momentum can be used. It is important to use the center of mass of the composite system as a reference and to calculate the rotational inertia of the "bar + clay" object. The orientation of the bar does not affect the calculations.
Felix83
On a frictionless table, a glob of clay of mass 0.38 kg strikes a bar of mass 1.76 kg perpendicularly at a point 0.12 m from the center of the bar and sticks to it.

If the bar is 0.66 m long and the clay is moving at 5.7 m/s before striking the bar, what is the final speed of the center of mass?

I found this part to be 1.012 m/s, which is correct, simply using conservation of linear momentum.

I can't figure out the next part:

At what angular speed does the bar/clay system rotate about its center of mass after the impact?

I tried using conservation of angular momentum, which seems to me like it should work, but the computer says it's wrong. I tried it assuming the center of mass doesn't change when the clay hits it, and then did it again figuring in the change in center of mass.

Is the bar initially vertical?

Felix83 said:
I tried using conservation of angular momentum, which seems to me like it should work, but the computer says it's wrong. I tried it assuming the center of mass doesn't change when the clay hits it, and then did it again figuring in the change in center of mass.
Conservation of angular momentum is the key. Using the center of mass of the composite system as your reference, calculate the angular momentum of the system before the collision. To find the angular speed after the collision, you'll need to find the rotational inertia of the "bar + clay" object about that center of mass.

Conservation of angular momentum is the key. Using the center of mass of the composite system as your reference, calculate the angular momentum of the system before the collision. To find the angular speed after the collision, you'll need to find the rotational inertia of the "bar + clay" object about that center of mass.

Thats what I did, the first time it was wrong, I just tried it again and now its right...figures.

It doesn't matter if the bar is vertical or horizontal, all you need to know is that the clay is coming in perpendicular to the bar.

Well its not clear what's going on, if the bar was standing vertically on a table and gets hit, it will rotate about its base, and there's a force of gravity adding to the angular velocity, so things would be more complicated.

## 1. What is the definition of conservation of momentum?

Conservation of momentum is a fundamental principle in physics that states the total momentum of a closed system remains constant over time, regardless of any internal or external forces acting on the system.

## 2. What is the difference between linear and angular momentum?

Linear momentum is the product of an object's mass and velocity in a straight line, while angular momentum is the product of an object's moment of inertia and angular velocity around an axis.

## 3. How does conservation of momentum apply to collisions?

In collisions, the total momentum of the objects before the collision is equal to the total momentum after the collision, as long as no external forces are present. This is known as conservation of momentum.

## 4. Can conservation of momentum be violated?

No, conservation of momentum is a fundamental law of physics and has been observed to hold true in all situations. If it appears to be violated, there is likely an external force acting on the system that has not been accounted for.

## 5. How does conservation of momentum relate to Newton's Third Law?

Newton's Third Law states that for every action, there is an equal and opposite reaction. This is directly related to conservation of momentum, as the momentum of the objects involved in the action and reaction must cancel out to maintain the total momentum of the system.

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