Newton’s Three Laws of Motion

a. The Three Laws

• First Law (Law of Inertia):
  An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless acted upon by a net external force.

• Second Law:
  The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass: $$ \vec{F}_{\text{net}} = m\vec{a} $$

• Third Law (Action–Reaction):
  For every force that object A exerts on object B, object B exerts an equal and opposite force on object A: $$ \vec{F}{A \text{ on } B} = -\vec{F}{B \text{ on } A} $$

b. Significance of the First Law

• Defines inertial reference frames: reference frames in which an object with no net force acting on it moves with constant velocity (including zero).
• Newton’s Second Law only holds in inertial frames. In non-inertial frames (e.g., an accelerating car), $\vec{F}_{\text{net}} \ne m\vec{a}$ unless fictitious forces are introduced.

c. Significance of Second Law

• Newton's first law is NOT the special case for the second law when $\vec{F}_{\text{net}} = 0$. It establishes the inertia reference frame, which is the condition where the second law is valid.
• $\vec{F}{\text{net}} = m\vec{a}$ establishes the cause and effect of motion. $\vec{F}{\text{net}}$ is the net force on the object, is the cause for the change of motion.
• $\vec{F}_{\text{net}} = m\vec{a}$ is only true in SI unit, in which the unit of force, Newton, or $N$, is defined such that the coefficient is 1, or $1 \text{N} = 1 \text{kg}\cdot{\text{m}}/{\text{s}^2}$.

c. Role of the Third Law

• Forces always occur in equal-and-opposite pairs between two interacting objects.
• The action and reaction forces act on different objects, so they do not cancel when analyzing a single object’s motion.