Why isn't linear momentum conserved?

[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?

 

[rcgldr]

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.

 

[IntegrateMe]

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?

 

[genericusrnme]

What does A/C mean?

 

[quietrain]

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.

 

[quietrain]

What does A/C mean?

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

 

[Redbelly98]

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.