Why isn't linear momentum conserved?

• IntegrateMe
In summary, the conservation laws of angular momentum and kinetic energy are applicable in this scenario, while the conservation of linear momentum is not due to the external force exerted by the pin on the rod during the collision. The correct options are A and C.
IntegrateMe
A ball of mass m elastically collides with a uniform rod of length L and mass 2m that is pinned at its center.

Which is/are conserved?

A. Angular Momentum
B. Linear Momentum
C. Kinetic Energy
D. A/C
E. All

The answer is D. Can someone explain why angular momentum is conserved and linear momentum isn't?

IntegrateMe said:
Can someone explain why angular momentum is conserved and linear momentum isn't?
Because the momentum of whatever the rod is pinned to (say the earth) is being ignored. The pin applies a force to something that isn't included as part of the problem statement.

Sorry, I may have an incorrect understanding of what exactly the linear momentum and angular momentum of a system are. Do you mind briefly explaining those as well?

What does A/C mean?

angular momentum is always conserve for collisions that do not involve external torques (i remembered my prof and tiny-tim saying something like that )

so the angular momentum of the horizontally moving ball, with respect to say the center of the rod , will be conserved as the angular momentum of the rod rotating as a result of the impact.

since the rod is pinned at the center, it has no translational movement, i.e it can't move horizontally. thus if the ball has linear momentum ( horizontal), then it will not be conserved because the rod doesn't move horizontally, its center of mass is fixed.

genericusrnme said:
What does A/C mean?

A/C means option A and C are correct :D

The linear momentum of a system is conserved if there are no external forces acting on the system. Since the pin exerts a force on the rod during the collision, linear momentum is not conserved.

Or ... you could consider the pin-plus-Earth as another rigid body that is part of the system -- as rcgldr suggested -- then linear momentum is conserved, however the momentum of Earth has not been included in calculating the momentum of the system.

1. Why is linear momentum not conserved in some systems?

Linear momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant over time. However, in certain systems, such as those involving external forces or collisions, linear momentum may not be conserved. This can be due to the transfer of momentum to or from the system, or the presence of non-conservative forces.

2. What factors can affect the conservation of linear momentum?

Several factors can affect the conservation of linear momentum, including external forces, collisions, and the presence of non-conservative forces. In some cases, the initial momentum of the system may also play a role in the conservation of momentum.

3. Can linear momentum be conserved in an open system?

No, linear momentum can only be conserved in a closed system, where there are no external forces acting on the system. In an open system, external forces can transfer momentum into or out of the system, causing a change in the total momentum of the system.

4. How can we determine if linear momentum is conserved in a given system?

To determine if linear momentum is conserved in a system, we must first identify all external forces acting on the system. If there are no external forces or if the net external force is zero, then linear momentum will be conserved. However, if there are external forces present, we must also consider the direction and magnitude of these forces to determine if momentum is conserved.

5. What are some real-life examples where linear momentum is not conserved?

One common example of linear momentum not being conserved is in a car collision. When two cars collide, the total momentum of the system changes due to the transfer of momentum between the cars. Another example is a rocket launching into space, where the propulsion of the rocket results in a change in the momentum of the rocket and the exhaust gases. In both cases, external forces are present that cause a change in the total momentum of the system.

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