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How can we know which frames are inertial and which arent?
Something I cant get my head around, if we have a simple 1D world, and frame A is accellerating to the right say wrt frame B. Then frame B is accellerating to the left wrt frame A, which one so how can we pick an intertial frame? Does this even make sense, what am I not understanding? I have vaguely heard it mentioned that there is no 'special' stationary frame (sounds reasonable), but then we could pick any frame and say it is inertial and just say every other frame accellerating wrt it is non inertial? how does this all work?
Edit: But why is the house the reference frame? What Im saying is that here we have two frames which are identical in every respect, so why should one be preffered over the other? I thought that was one of the main points of relativity, there is no preffered frame?
2 Answers
- Anonymous8 years agoFavorite Answer
As in your example, lets assume frame A accelerating to the right wrt frame B.
Then frame B is accellerating to the left wrt frame A, correct, let's say with acceleration +a units.
But if you are studying a mechanical system in frame B, and you want to find your results with respect to frame B itself, then you would apply a pseudoforce to every element in frame B, giving each mass an acceleration of -a units, ie a rightward acceleration.
Picture yourself in a bus (frame B) accelerating wrt to your house (frame A) with acceleration +a units (towards the right).
Like so:
(House) . . . . . . . .[BUS . . (you). . .]
A B
If you are sitting in the bus (assume a frictionless floor), you see a toy car on the floor of the bus accelerating backwards. This acceleration is seen only to you in the bus.
To your mother sitting at home, there would be no net force acting on the toy car, and it would not change its position relative to the house. Zero velocity, zero acceleration wrt to Frame A, the house.
But wrt to the accelerating frame B, it does have an acceleration due to pseudoforce.
Now, think in the reverse. Your house is accelating at -a units with respect to the bus. You, sitting in the bus, think that you are stationary and that your house is accelerating away from you.
But if your mother places a toy car on the (frictionless) floor of the house, there is no pseudoforce on it. Why? Because a non inertial frame is one which is accelerating WITH RESPECT TO A GROUND FRAME, or REFERENCE FRAME, which can be assumed not to be accelerating itself. For our purposes, we usually consider the earth's frame to be an inertial reference frame, as its acceleration has no influence on physics on earth.
And so, the bus is a non inertial frame wrt to the house, which is a part of the inertial GROUND FRAME. But not vice versa. I hope this cleared things up a little bit, I'm no expert, this is how I understand things.