# Newton's Laws¶

## Newton's First Law (Inertia)¶

An object at rest will stay at rest, and an object in motion will stay in motion unless acted on by a net force.

Mathematically, this is equivalent to saying that if the net force on an object is zero, then the velocity of the object is constant.

$$\large \vec{F} \ = \ m\frac{d\vec{v}}{dt} \ = \ 0 \quad \quad \rightarrow \quad \quad \vec{v} \ = \ \text{constant.}$$
• GRE Physics GR0877 Problem 001

## Newton's Seond Law (Force)¶

The rate of change of momentum of a body over time is directly proportional to the force applied, and occurs in the same direction as the applied force.

$$\large \vec{F} \ = \ m \frac{d^2 \vec{x}}{d t^2} \ = \ m \frac{d \vec{v}}{dt} \ = \ m\vec{a}$$
• GRE Physics GR1777 Problem 001

## Newton's Thrid Law (Action-reaction law)¶

All forces between two objects exist in equal magnitude and opposite direction.

$$\large F_{12} \ = \ - F_{21}$$