Newton's Laws of Motion

Newton’s deepest insight is what does not need explaining: steady motion needs no force at all. Forces explain changes in motion. Ask "what net force acts?" and you know the acceleration; ask "what acceleration do I see?" and you know the net force. The second law runs in both directions.

Newton's three laws form the foundation of classical mechanics.

The laws

1. First law (Inertia): A body remains at rest or in uniform motion unless acted on by a net external force.
2. Second law: $\vec{F}_{\text{net}} = m\vec{a}$
3. Third law: If body A exerts a force on body B, then B exerts an equal and opposite force on A.

Free-body diagrams — The essential tool for applying Newton's laws:

1. Isolate the object.
2. Draw all forces acting on it (weight, normal, tension, friction, etc.).
3. Choose coordinate axes (often along and perpendicular to the surface).
4. Apply $\sum F_x = ma_x$ and $\sum F_y = ma_y$.

Common forces

Key insight: Newton's second law is not $F=ma$ — it is $\vec{F}_{\text{net}}=m\vec{a}$. Only the vector sum of all forces determines acceleration.

Common pitfall: Action–reaction pairs never cancel, because they act on different bodies. The book’s weight and the table’s normal force on it are NOT such a pair — both act on the book; its true partner forces act on the Earth and the table.