# Conservation of linear, angular momentum and energy in a collision

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1. Nov 13, 2014

### paalfis

1. The problem statement, all variables and given/known data
Mass 2 collides with mass 1 as shown in the image, mass 1 is attached to the stick and it is initially stationary. Consider that the stick is massless and can rotate around the point O. The entire system is on a frictionless table.
Which magnitudes are conserved in the system {m1,m2} before, during and after the collision?

Comments: no information is given (at this stage of the problem) about what kind of collision we are talking about.

3. The attempt at a solution

Before the collision:

• External Forces sum up to zero-->Linear Momentum is conserved.
• For the same reason, angular momentum with respect to O is conserved.
• There are not any non conservative forces in the system-->Mechanical energy is conserved.
During the Collision:
• The bar exerts a force on the ball (Tension) --> linear momentum is not conserved.
• The tension is a central force --> Angular Momentum is conserved.
• The Tension is perpendicular to the movement of m2, so energy is conserved.
After the collision: I think it is exactly the same as during the collision, is this ok?

The next question is, in which direction does m2 move after the collision.

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Last edited: Nov 13, 2014
2. Nov 13, 2014

### haruspex

It's only perpendicular to the subsequent movement. You cannot apply that at the instant of collision. It is not stated whether the collision between the masses is elastic, but if the rod is rigid and an impulse 'tries' to change its length then that is effectively an inelastic collision.