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In my notes, it says that the total change in momentum of an inertial reference frame is zero. Please see the picture below

enter image description here

This has confused be because

  • I nnderstand that the inertial reference frame itself, by definition, cannot be accelerating. So for example if someone is looking out of their accelerating car, what they see is not an inertial reference frame.

  • however I do not understand that the total change in momentum will be zero. If someone is looking out of their car now moving at constant velocity (or stationary or whatever! It is now an inertial reference frame), could they not see an object that they are viewing in their inertial reference frame be accelerating because there is a net force acting of it? For example, they are watching an accelerating train which is accelerating in their own inertial reference frame?

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The total momentum the notes are talking about is the net momentum of all the particles. In whichever way the particles collide or interact with each other, they total change in momentum is 0 as the forces exerted by the particles on each other are internal forces. There are no net external forces here. If we observed this system from a non inertial reference frame, there would be a pseudo force acting on all the particles which is an external force and hence there would have been a change in the total momentum.

Yes one can see an object accelerating in an inertial reference frame, if it has some force is being exerted on it. But in the earlier example of a system of particles there were no net external forces. From any inertial reference frame, the net momentum of the particles will remain constant. But from a non inertial frame, one can see objects which don't experience any net external force with respect to inertial frame accelerate due to the pseudo force. Eg - A ball lying on the ground doesn't experience any net external force. From whichever inertial frame you observe the ball, it won't have an accelerated motion. Eg - A lift going up at a constant velocity. But from a non inertial frame , the ball will appear to be accelerated.

An object which doesn't accelerate in an inertial frame won't accelerate in any other inertial frame but will in a non inertial one due to the pseudo force.

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The author is implying that within a given inertial reference frame, and only within that reference frame, no outside forces are acting, or the frame wouldn't be inertial. With this being the case, inside that reference frame, there can only be a change in momentum of a particular object if there is an equal and opposite change in momentum in the object that caused this change, due to Newton's 3rd law. Accordingly, the sum of all the momenta changes within the inertial reference frame must be zero, which is what the equation that you drew the box around is saying.

Regarding the example of looking out a car window that is traveling at constant velocity, you are attempting to observe an object that is outside the stated inertial reference frame. That situation is not what the text is describing.

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