Foundations — Free body diagrams — systematic drawing technique

Everything on the parent page rests on a small pile of ideas. Below, each one is built from nothing: plain words → a picture → why the topic can't live without it. They are ordered so each new idea only uses ideas already built.

1. A "body" and shrinking it to a dot

Before you draw anything, you must circle one thing and mean it. If you circle the whole table-plus-block, the table's forces become internal and invisible. If you circle only the block, the table becomes environment and its push on the block becomes a force you must draw.

The picture: we pretend the object's shape doesn't matter and squash it to a single point — a dot. Why is that legal? Because for sliding/translating motion (not spinning), every part of the object moves together, so we only care about where the object is, not its outline.

Why the topic needs it: the whole recipe is "forces on the dot." Without a firmly chosen dot, "on" has no meaning.

2. Force — a push or a pull, drawn as an arrow

An arrow that carries both a size and a direction is called a vector. You cannot describe a force with one number alone — "10" means nothing until you say "10 units, pointing left." That is exactly why we use arrows and not plain numbers.

Why the topic needs it: the FBD is a collection of force-arrows. See Resolving Vectors into Components for how one arrow becomes two numbers.

3. Mass $m$ — how much "stubbornness" an object has

The picture: a shopping trolley empty vs. full. The full one is harder to get moving and harder to stop. That "harder-ness" is mass.

Why the topic needs it: mass is the bridge between the force-arrows and the resulting motion. Small force + big mass = tiny acceleration.

4. Acceleration $\vec{a}$ — the change of motion, NOT motion itself

This is the trickiest zero-point, so slow down. Velocity is "how fast and which way you're going right now." Acceleration is "how fast that velocity is being altered." A car cruising at a steady 100 km/h has huge velocity but zero acceleration. A car just leaving the lights has small velocity but large acceleration.

Why the topic needs it: the right-hand side of ${\vec{F}}_{net}=m\vec{a}$ is acceleration. This is also why the parent warns you never to draw "$m\vec{a}$" as an arrow — it is the effect, computed after the arrows are added, not one of the pushes. See Newton's Second Law.

5. Gravity and weight $W=mg$ — the always-on downward pull

Two new letters here:

• $m$ = mass (built in §3).
• $g$ = the strength of Earth's gravity per kilogram, about $9.8{\text{m/s}}^2$. Multiply mass by $g$ and you get the pull in newtons.

The picture: an invisible rope from the object straight down into the Earth's centre. It never touches anything to work — it acts at a distance (a long-range force). That is why the recipe draws it first: it is present in every single problem and easy to forget precisely because nothing is touching the object to remind you.

6. The four contact forces: $N$, $f$, $T$, $F$

Forces only appear where the body touches something (or via gravity). So walk around the boundary of your dot; every touch is a force. There are four flavours the parent uses.

Why the topic needs all four: they are the entire "N-F-T-A" checklist from the parent's mnemonic. See Normal Force and Friction and Tension in Strings and Pulleys.

7. Newton's Third Law — why the reaction is NOT on your FBD

The picture: you lean on a wall (you push the wall right), the wall pushes you left. Both arrows exist — but one is on the wall, the other is on you. Your FBD is "forces on you," so only the wall's push on you belongs there. The push you exert on the wall lives on the wall's FBD.

Why the topic needs it: this is the #1 way beginners over-crowd a diagram. Knowing the pair splits across two bodies keeps each FBD honest. See Newton's Third Law.

8. Splitting arrows into axes: $\sum F_x$, $\sum F_y$

Once arrows are drawn, adding them "by eye" is guesswork. So we lay down two guide-lines (axes): one horizontal ($x$), one vertical ($y$). Then every arrow is described by two ordinary numbers: how much it pulls along $x$, and how much along $y$.

The symbol $\sum$ (Greek capital "sigma") just means add them all up. So $\sum F_x$ = "add up the $x$-parts of every force."

Why the topic needs it: this is how the drawing becomes algebra. Read more in Resolving Vectors into Components.

The prerequisite map

Read it top-down: choosing a body and understanding force-arrows lets you place weight and contact forces; the third law stops you drawing reaction forces on the wrong body; mass and acceleration wait on the right-hand side; splitting into axes finally turns the picture into solvable equations — the destination is the FBD recipe.

Equipment checklist

Cover the right side and test yourself. Each should be an instant "yes, I can picture it."