I would like to explore Newton’s laws in a bit more detail, especially the connection between the two different versions that I introduced in my previous post. Whereas that post focused on “higher-level” aspects of Newton’s laws, this one will explain some of the supporting details. (I’m also sort of making this post for the sake of completeness: I made a claim in my previous post, and I want to prove it. You shouldn’t believe anyone’s claims unless they have proof, including me.)
Just as a reminder, Newton’s Laws of Motion are:
- If there is no net force on an object, it will have no acceleration.
- If there is a net force
acting on an object with momentum
, then
.
- If object 1 exerts a force on object 2, then object 2 exerts a force on object 1 with the same magnitude but opposite direction.
I plan to turn them into:
- The other two laws are valid in only in inertial reference frames. These special frames really do exist, and they are easy to identify.
- There is an equation (
) that can determine the position and velocity of an object at any time in the past or future.
- The momentum of a system is conserved if no forces act on it.
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