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.

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

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