Consider the vector-valued velocity as a function of time, v:t↦R3. Scale this by the object’s mass and you get the momentum function over time. Imagine this momentum function wiggling around over time, the vector from the origin rotating and growing and shrinking.
The third law says that force is the derivative of this rescaled vector function—if an object is more massive, then the same displacement of this rescaled arrow is a proportionally smaller velocity modification, because of the rescaling!
And also, forces have opposite reactions (by conservation of momentum) and equal reactions (by conservation of energy).
Epistemic status: not an expert
Understanding Newton’s third law, F=ddt(mv).
Consider the vector-valued velocity as a function of time, v:t↦R3. Scale this by the object’s mass and you get the momentum function over time. Imagine this momentum function wiggling around over time, the vector from the origin rotating and growing and shrinking.
The third law says that force is the derivative of this rescaled vector function—if an object is more massive, then the same displacement of this rescaled arrow is a proportionally smaller velocity modification, because of the rescaling!
And also, forces have opposite reactions (by conservation of momentum) and equal reactions (by conservation of energy).