Sir Isaac Newton's Laws of Motion

First published in 1686

Amazon : Philosophiae Naturalis Principia Mathematica
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First Law of Motion

aka The Law of Inertia

Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion continues with constant velocity in the same direction unless acted upon by an unbalanced force.

In every material universe, the motion of a particle in a preferential reference frame Φ is determined by the action of forces whose total vanished for all times when and only when the velocity of the particle is constant in Φ. That is, a particle initially at rest or in uniform motion in the preferential frame Φ continues in that state unless compelled by forces to change it.

Newton's first and second laws are valid only in an inertial reference frame. Any reference frame that is in uniform motion with respect to an inertial frame is also an inertial frame, i.e. Galilean invariance or the principle of Newtonian relativity

Second Law of Motion

Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.

The second law states that the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force.

Momentum (p) is velocity times mass.

so

This is commonly remembered as F = ma

Impulse (J) occurs when a force acts over a time interval.

so Impulse = Force x Time

Impulse is the change in momentum.

Third Law of Motion

Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.

All forces between two objects exist in equal magnitude and opposite direction: if object A exerts a force F_A on object B, then B simultaneously exerts a force F_B on A, and the two forces are equal in magnitude and opposite in direction: F_A = −F_B .

Here, F_A is the action and F_B is the reaction.

© Alexander Forrest