Newton's third law states that each force has an equal and opposite force. If I kicked a ball, it would apply the same force on me. Is this due to the ball's inertia? To clarify, is the ball exerting a force on me because it wants to stay in its original position?
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2related: https://physics.stackexchange.com/q/66057/ – leongz Apr 27 '18 at 21:39
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Newton's third law is a consequence of conservation of momentum, which we have never been able to falsify. Consider a system of two particles with total momentum $\vec P$ such that
$$ \vec P = \vec p_1 + \vec p_2. $$
Noting the relationship between force and impulse, $\vec F = \frac{d\vec p}{dt}$, we can take a time derivative to find
$$ \frac{d\vec P}{dt} = \frac{d\vec p_1}{dt} + \frac{d\vec p_2}{dt} = \vec F_{\rm 2\, on\, 1} + \vec F_{\rm 1\, on\, 2}. $$
If the total momentum is conserved, then $\frac{d \vec P}{dt} = 0$, and we have $$ \vec F_{\rm 2\, on\, 1} = - \vec F_{\rm 1\, on\, 2}.$$
The ball exerts a force back on you in order to conserve linear momentum.
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I don't disagree with that, but in your derivation, you rely on the relationship F=dp/dt for each particle, which does not seem to be valid in the static case. – V.F. Apr 28 '18 at 14:41