Newton's Laws

Principle of Inertia §

In the absence of force, an object stays at rest or in uniform motion.

Force Law §

An object will accelerate proportionally to the force applied

$$\vec{F}=m\vec{a}$$

Action/Reaction §

The force exerted on object 1 by object 2 is equal and opposite to the force exerted on object 2 by object 1.

$${\vec{F}}_{12}=-{\vec{F}}_{21}$$

Equilibrium of Forces §

$$\vec{F}=\sum _i{\vec{F}}_i=0=m\vec{a}⟹\vec{a}=0$$

Torque §

\vec{\tau} = \vec{r} \times \vec{F} = I\vec{\alpha} ,$$