Show that Newton's second law is the only real law of motion.

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> [!TLDR]
> The first and third laws can both be derived from the second law (F = dp/dt), which is why the second law is often called the only truly independent (real) law of motion.
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> Newton's second law states: F = dp/dt (net external force equals the rate of change of momentum).
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> 1) First law follows from the second law:
> If no net external force acts on a body, F = 0, so dp/dt = 0, which means p (momentum) is constant. For a body of constant mass this means its velocity is constant - i.e. it continues in its state of rest or uniform motion in a straight line. This is exactly Newton's first law, so the first law is simply the special case of the second law when F = 0. (In fact, the first law is used to define what an inertial frame is, in which the second law is then applied - but its content as a statement about motion is subsumed by the second law.)
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> 2) Third law follows from the second law + momentum conservation:
> Consider two isolated bodies 1 and 2 interacting only with each other, so the total momentum of the system, p1 + p2, is conserved (no external force):
> d(p1 + p2)/dt = 0
> dp1/dt + dp2/dt = 0
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> By the second law, dp1/dt = F21 (force on body 1 due to body 2) and dp2/dt = F12 (force on body 2 due to body 1). So:
> F21 + F12 = 0
> F21 = -F12
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> This is exactly Newton's third law: the force body 2 exerts on body 1 is equal and opposite to the force body 1 exerts on body 2.
> …

Q.Show that Newton's second law is the only real law of motion.

Concept understanding — Newton Second Law

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The Precise Statement

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A Simple Example

Q.Show that Newton's second law is the only real law of motion.

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