# Momentum and Inertial Reference Frame

1. Sep 27, 2016

### jjkim623

1. The problem statement, all variables and given/known data
At the roller rink, two 20-kg girls accelerate toward each other until they are each moving at 2.7 m/sin the Earth reference frame. They then collide stomach-to-stomach, grab on to each other, and fall to the floor.

A. Calculate the magnitudes of the momentum of each girl before the collision in the reference frame of a mother who started skating with one of the girls and then continued on after the collision without changing speed. Denote the momentum of the girl that moves with the mother as p1 and the momentum of other girl as p2.

B. Calculate the magnitudes of the momentum of each girl after the collision in the reference frame described in part B.

2. Relevant equations
p=mv

3. The attempt at a solution
A. If the girl moving with the mom is using the mom as a reference frame, then |p1|=0 since her velocity is 0 relative to the mom. The part I'm stuck on is how to figure out |p2| given an inertial frame of reference that's moving. Despite using the mom as the inertial reference frame versus the Earth, wouldn't conservation of momentum imply that relative to the mom....

p1initial + p2initial = p1final + p2final

and if

pfinal= 20*(-2.7) + 20*-2.7= -108 kg*m/s2

then

pinitial= 20*0 + 20v2,f= -108 kg*m/s2

so

|p2initial| = |20v2,f| = |-108|= 108 kg*m/s2

B. If both the girls have a velocity of zero (relative to the Earth), but the mom is moving away to the right, then that would mean that relative to the mom, the girls would be moving to the left. Therefore, the momentum of the each girl relative to the mom would be p= m(-v)= (20)(-2.7)= -54, but because the question is asking for magnitude, the answer is +54.

Is my thinking correct?

Last edited: Sep 27, 2016
2. Sep 27, 2016

### jbriggs444

[Total] momentum [in a closed system] is a conserved quantity. That is, it does not matter when you look, the total momentum is always the same.

[Total] momentum [in a closed system] is not an invariant quantity. It does matter what frame of reference you use when you look. The total momentum can change depending on your choice of reference system.

As you note, the girl clearly has zero momentum in a frame of reference where she is motionless. And non-zero momentum otherwise.