00:01
Okay, for this question we're proving that the law of conservation of momentum is invariant under galilean transformation.
00:06
So the law of conservation states that the total momentum of a closed system remains constant with no external forces.
00:12
Gallian transformation is the mathematical transformation that describes the relationship between two reference frames that are moving relative to each other at constant velocity.
00:22
So to prove that the law of conservation of momentum is invariant under galilean transformation, we need to show that the total momentum of a closed system remains constant in both frames.
00:32
So let's consider a closed system of two particles, okay, with mass one and mass two moving with velocity one and velocity two respectively with respect to the first frame.
00:45
So the total momentum of the system with the first frame, okay, momentum one is m1 v1 plus m2 v2.
00:56
Let's transform to the second reference frame that's moving in constant with velocity u relative to the first frame.
01:02
The velocities of the particles in the second reference frame are therefore v1 dash which is equal to v1 minus u and v2 dash which is equal to v2 minus u.
01:17
So the total momentum of the system in the second reference frame is given by momentum two, which is m1 v1 minus u plus m2 v2 minus u.
01:32
Okay, and we can also write this as m1 v1 plus m2 v2 minus m1 plus m2 times u...