“The laws of physics are independent of frame of reference if the two frames of reference are moving one relative to the other at a constant velocity.”
A velocity of zero counts as a constant velocity.
Galilean Transformation
A transformation that takes you from one frame of reference to another frame of reference is it Galilean transformation if the difference between those two reference frames is constant motion.
We can come up with a list of things that we do that demonstrate the law of physics. We can drop a ball, toss it up into the air, etc. We might do some tricks with a pool table. Can you think of any other tricks?
Now, we go on a train that is moving at a constant speed and do all the experiments mentioned above and inside the train, the results are the same. Oh, and this train is made out of a very transparent polymethylmethacrylate so someone on the ground watching the train go by gets different results. As an example, you toss a ball straight up into the air and then it comes back down and lands in your hand. The person on the ground sees the ball travel a path that is a parabola with horizontal movement as well as the moving up and down (vertical).
The train is moving in the x direction.
- x’ = x + vt
- y’ = y
- z’ = z
- t’ = t
A person in a moving train throws a ball up into the air and collects values for for y (height above the floor) along with t.
- (0, 0, 0, 0)
- (0, 45, 0, 1)
- (0, 80, 0, 2)
- (0, 105, 0, 3)
- (0, 120, 0, 4)
- (0, 125, 0, 5)
- (0, 120, 0, 6)
- (0, 105, 0, 7)
- (0, 80, 0, 8)
- (0, 45, 0, 9)
- (0, 0, 0, 10)
For the person on the ground, they see the train moving 20 feet per second in the x direction, and their coordinates are as follows:
- (0, 0, 0, 0)
- (20, 45, 0, 1)
- (40, 80, 0, 2)
- (60, 105, 0, 3)
- (80, 120, 0, 4)
- (100, 125, 0, 5)
- (120, 120, 0, 6)
- (140, 105, 0, 7)
- (160, 80, 0, 8)
- (180, 45, 0, 9)
- (200, 0, 0, 10)
Appendix A
For Galileo, time is absolute, so t’=t. This will change when we get to Special Relativity, where the speed of light is constant and the speeds of clocks (which measure time) must change, one relative to the other.
Appendix T
Mockingbird students are looking into it: we may have an opportunity here to study several types of transformations and do a compare and contrast.
Rob Sterling 