# Why Isn't Linear Momentum Conserved?

• student34
In summary, a thin metal bar with a length of 2.00 m and a mass of 9.18 kg is hanging from a ceiling by a frictionless pivot. It is struck 1.50 m below the ceiling by a 3.00 kg ball traveling horizontally at 10.0 m/s. The ball rebounds in the opposite direction with a speed of 6.00 m/s. The angular speed of the bar after the collision is 5.88 rad/s. The angular momentum is conserved during the collision, but not the linear momentum due to the tension and gravity forces at the pivot point. The momentum is only conserved if the entire system is considered, not just a part of it.
student34

## Homework Statement

A thin metal bar, 2.00 m and a mass of 9.18 kg hangs vertically from a ceiling by a frictionless pivot. Suddenly it is struck 1.50 m below the ceiling by a small 3.00 kg ball, initially traveling horizontally at 10.0 m/s. The ball rebounds in the opposite direction with a speed of 6.00 m/s.

(a) Find the angular speed of the bar just after the collision. ***The answer in the textbook is 5.88 rad/s, and that makes sense to me.***

(b) During the collision, why is the angular momentum conserved but not the linear momentum?

## Homework Equations

m*v(initial)*l = Iω + m*v(final)*l

## The Attempt at a Solution

I have absolutely no idea how this is possible. I was always taught that momentum is always conserved.

What are forces at the pivot point?

Borek said:
What are forces at the pivot point?

There are tension and gravity forces, but I don't understand how they would affect the linear momentum of the ball in the horizontal dimension.

student34 said:
There are tension and gravity forces, but I don't understand how they would affect the linear momentum of the ball in the horizontal dimension.
Hint: Does the pivot move? Why not?

It would be useful here to keep in mind what criteria need to be met for linear momentum to be conserved.

Linear momentum is conserved (if you consider the whole system).

Linear momentum is not necessarily conserved (if you only consider part of the system).

E.g. bouncing ball: momentum conserved if you consider the Earth's momentum; momentum clearly not conserved if you consider the ball only.

Yeah, I should have knew that, thanks everyone!

## 1. Why is linear momentum important in physics?

Linear momentum is important in physics because it is a fundamental property of moving objects that helps us understand and predict their motion. It is a conserved quantity, meaning it remains constant unless an external force acts on the object. This allows us to apply the principle of conservation of momentum to analyze collisions and interactions between objects.

## 2. What does it mean when linear momentum is conserved?

When linear momentum is conserved, it means that the total momentum of a system remains constant. In other words, the initial momentum of the system before any interactions or collisions is equal to the final momentum after the interactions or collisions. This is a fundamental principle in physics that applies to all isolated systems.

## 3. What factors can cause linear momentum to not be conserved?

Linear momentum can be not conserved if an external force is applied to the system, causing a change in the momentum of the objects. This can also occur if there are external forces such as friction or air resistance acting on the objects, which can change the velocity and therefore the momentum of the objects.

## 4. Can linear momentum be conserved in an elastic collision?

Yes, linear momentum can be conserved in an elastic collision. In an elastic collision, the total kinetic energy of the system is conserved, meaning there is no loss of energy. This allows for the conservation of both linear momentum and kinetic energy, making it a more ideal and efficient type of collision.

## 5. Why might linear momentum not be conserved in an inelastic collision?

Linear momentum may not be conserved in an inelastic collision if there is a loss of kinetic energy during the collision. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound, causing a decrease in the total kinetic energy of the system. This decrease in kinetic energy can result in a change in the momentum of the objects, causing it to not be conserved.

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