Forces, Newton’s Laws, and Free-Body Diagrams

Manual: General · Subject: Applied Physics

Use force models and free-body diagrams to analyze equilibrium and motion in real systems.

Newton’s Laws in Practice

Core laws

Newton’s first law describes inertia, the second law relates net force to acceleration with $\sum \vec{F} = m\vec{a}$ , and the third law states that forces come in equal and opposite pairs acting on different bodies.

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Common mistake

Action-reaction pairs do not cancel each other because they act on different objects.

Free-Body Diagrams

How to build a free-body diagram

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Step 1: Isolate the object of interest.
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Step 2: Draw every external force acting on it.
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Step 3: Choose coordinate axes that simplify the forces.
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Step 4: Resolve angled forces into components.
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Step 5: Apply $\sum F_x = ma_x$ and $\sum F_y = ma_y$ as needed.

Common forces

Weight

mg

downward

Normal force

Perpendicular contact force

Tension

Pull transmitted by a string or cable

Friction

Force opposing relative motion or slipping

Spring force

F = -kx

A block rests on a table. Which force balances its weight?

Friction Tension Normal force Air resistance

What does $\sum \vec{F} = 0$ mean physically?

Friction and Contact Forces

Friction model

Static friction adjusts up to a maximum value $f_s \le \mu_s N$ , while kinetic friction is often approximated by $f_k = \mu_k N$ . These models are simplifications, but they are very effective in many engineering estimates.

Which friction force typically has the larger maximum value?

Kinetic friction Static friction They are always equal Neither can be compared

Why are free-body diagrams valuable in mechanics?

Neuroanatomy Explorer

Memory Deck

Match the Pairs

Concept Constellation