Free-Body Diagram Builder

Source

Lecture: L4 — Forces & Newton's Laws (companion to the Forces on Objects Explorer)
Simulation: Free-Body Diagram Builder — reusable tool, embeddable inside other sims
Concept: Every real force on a body is attributed to an agent; F_net = Σ F_i = m a decides the motion.
Serves: Identifying particles and the real forces on each; predicting motion from a self-built FBD before net-force reveal.
Inquiry: Orient → Build (agent-labelled arrows) → Predict acceleration → Check against known-good solution.
Misconception target: Inventing agent-less forces (e.g. "force of motion"); confusing centripetal (real, inward, inertial frame) with centrifugal (fictitious, outward, rotating frame); confusing third-law pairs (they act on different bodies); omitting fictitious forces in a rotating frame.
Notation: F_g = mg for gravitational weight; N = normal; T = tension; f = friction; F_app = applied contact push/pull; F_cf = centrifugal (rotating frame only); F_cor = Coriolis (rotating frame only). Canvas angle convention: 0° = right, 90° = up.

Pedagogy principles applied

ID	Principle	How it shows up here
Predict-first	Prediction before reveal	The net-force vector is hidden until the student commits the FBD.
H1/H2	Structural misconception	Wrong-force rebuttals appear only when a spurious/mis-agented arrow is committed — not as standing text.
D7	Progressive reveal	Panels appear as the inquiry step requires them, not all at once.
D2	Readable canvas labels	Each arrow carries its symbol + agent on the canvas; no separate wall of text.
D8	Numeric entry	Magnitude and angle accept typed values — dragging alone was too finicky in L4.
A3/A4	Formal off by default	Equations (F_net = ma, mg sin θ / mg cos θ, rotating-frame terms) live in ⚛︎ The Physics — the pop-up revision sheet.
E1	Animation honesty	The body only moves after the FBD is checked; it doesn't loop at the canvas edges. Animation time is scaled by ×6 for visibility (a numeric readout uses true m/s²).
Frame	Reference frame	Rotating/circular scenarios require choosing inertial vs rotating before building.

Teach me

Speed

Scene — block on table (rest)

↑ F_g gravity · ↑ N normal

↑ T tension · ↑ f friction

↑ F_app applied · ↑ F_cf / F_cor fictitious

drag outward from the dashed body to draw a force arrow

Guided Inquiry

1 · Orient to the scenario

Let’s begin by reading the scene at the top of the canvas: a block sitting on a table, at rest. First, spot the body — the thing whose FBD you'll build (it’s highlighted with a dashed outline and labelled "body").

Before you start drawing arrows, here’s a question worth asking every time: is this scenario in an inertial or rotating frame? What do you think?

2 · Build the FBD

Now for the heart of it. Which forces do you think act on this block?

Now draw them. Click and drag from the body to place a force arrow (or use ＋ Add force arrow in the Force arrows panel). An editor pops up at the arrow, so you can pick its type and agent with one click each. Remember, every arrow needs an agent before the diagram can be checked.

3 · Predict the motion

Now let’s put your diagram to work. From your FBD (the net force is still hidden), which way — if at all — do you think the block accelerates?

4 · Check & reveal

Time to see how you did. Checking the diagram reveals the net-force vector (the thick white arrow) and grades your FBD against the known-good solution.

For this block on a table, you should end up with two real forces (gravity from Earth ↓, and normal from the table ↑). If they’re not on your diagram yet, add them now, then press the button:

5 · Free build

Nice work — that’s the guided part done. Now pick any scenario and keep building. If you’d rather explore freely without grading, untick Grade my diagram (in the Check & result panel).

Don’t worry if you slip up — reminders will pop up in the grading banner when they’re relevant: every arrow needs an agent, and third-law pairs act on two different bodies.

Listen

Scenario

▾

Switching scenario clears your arrows.

Mass m (kg)2.0

Incline angle θ (°)25

Angular speed ω (rad/s)1.0

Applied force |F_app| (N)5.0

Reference frame

▾

Non-rotating — use the inertial frame.

Force arrows

▾

Force arrows0

No arrows yet — drag from the body or use ＋ below.

0° = right · 90° = up. Every arrow needs an agent (what exerts it).

Check & result

▾

Grade my diagram

Untick to explore without grading.

Diagram checkedno

Net force on the body

|F_net| — N

direction 0° = right · 90° = up

—

|a| |F_net| / m

— m/s²

After a correct check · animation ×6, readout true |a|

Newton's 2nd law — vector sum of real forces sets the acceleration:

Incline decomposition (gravity along + into slope, both frame-invariant magnitudes):

Third-law pair — acts on two different bodies:

Rotating-frame fictitious forces (declare frame first):

The Physics

Free-body diagrams · what this sim shows, the physics behind it, and every control

At a glance

A free-body diagram shows one body and every force acting on it, one arrow per force, each with a named agent. This sim has you build the diagram, then checks it and reveals the net force, so you can test your reading of a situation against Newton's second law.

What you'll learn

How to decide which forces belong on a diagram, and what an agent is.
How the arrows combine into a net force, and what that says about the motion.
How the directions and sizes of the forces are set on an incline.
How the diagram for circular motion depends on the reference frame.

One force arrow, as the sim draws it.

What's on screen

The body (dashed outline, labelled "body"): the object whose diagram you build.
Force arrows, coloured by type: gravity blue, normal green, tension amber, friction pink, applied violet, fictitious red. Each carries its symbol and agent.
Net force arrow: the vector sum of your arrows. It appears only after you check the diagram.
Check & result panel: a grading banner, then |F_net|, its direction and |a|.

See itDraw one sample arrow and open its editor. Watch for: the arrow labelled with its symbol and agent, and the editor beside it with the type, agent, size |F| and angle θ.

The controls

Press ⌖ on a row to see where that control sits in the sim.

Control	What it changes	Range
Scenario	Which situation the body is in. Switching clears your arrows.	6 scenarios opens on Block on table
Mass m	The body's mass, which sets its weight and its acceleration for a given force.	0.5–10 kg opens at 2.0 kg
Incline angle θ	The slope of the surface. Shown in the incline scenario only.	0°–60° opens at 25°
Angular speed ω	How fast the body circles its centre. Shown in the orbit scenario only.	0.2–3 rad/s opens at 1.0
Applied force \|F_app\|	The push of box A on box B. Shown in the two-body scenario only.	1–20 N opens at 5.0 N
Reference frame	Inertial or Rotating. Rotating can be chosen in the orbit scenario only.	2 buttons opens on Inertial
＋ Add force arrow	Adds an arrow. You can also drag outward from the body. The editor sets its type, agent, size \|F\| and angle θ.	θ: 0° = right, 90° = up
Clear arrows	Removes every arrow so you can start the diagram again.	button
Grade my diagram	On: the check grades your arrows. Off: it only reveals the net force.	on / off opens on
✓ Check diagram	Reveals the net force, then moves the body along it.	button
Net force readouts	\|F_net\|, its direction and \|a\| = \|F_net\|/m, filled in by the check.	panel
▶ Play / ⏸ Pause	Pauses the motion that follows a check, so you can compare positions.	top bar
Speed	Plays that motion faster or slower on screen.	0.25×–4×
↻ Reset	Restarts the mode you are in from its beginning.	top bar

Fixed: g = 9.8 m/s², static friction μ_s = 0.6 on the incline, orbit radius r = 2 m. The check accepts an arrow within ±15° and ±15% of the correct one.

Every arrow needs an agent

A free-body diagram isolates one body and shows only the forces on it. Each arrow is one interaction, and the agent is the object that exerts it.

Contact forces come from something touching the body: a table, a string, a hand, another box. Gravity, from Earth, is the one force here that acts at a distance.
No agent, no arrow. "Motion", "momentum" and "inertia" exert nothing. A ball in flight, with air drag ignored, has one arrow: gravity.
Forces the body exerts on other objects do not appear on its diagram.

A block of mass 2 kg on a table: two agents, two arrows, drawn to one scale.

Key idea. Count the agents touching or pulling the body. Each one gets one arrow.

See itBuild the block's diagram with its two agents, then check it. Watch for: the check turning green, with the Net force reading 0.00 N (balanced).

The net force sets the motion

The check adds your arrows as vectors. Newton's second law turns that sum into an acceleration:

Newton's second law.

Balanced arrows: F_net = 0, so a = 0. The body stays at rest or keeps a constant velocity.
Unbalanced arrows: a = F_net/m, in the direction of F_net.
On the sim's incline, gravity and the normal force alone leave F_net = mg sinθ down the slope. At 25° that gives a = g sinθ = 4.14 m/s², whatever the mass.
After a correct check the body moves along F_net. The animation runs 6 times faster than real time. The |a| readout is the true value.

See itOn a 25° incline, draw gravity and the normal force only, then check. Watch for: Net force 8.28 N pointing down the slope, a = 4.14 m/s², and the block sliding.

Directions and sizes on an incline

Gravity points straight down, size mg. Tilting the slope never rotates it.
The normal force is perpendicular to the surface, so it leans away from vertical by θ. Its size is mg cosθ.
Friction lies along the surface. It takes whatever value holds the block, up to the limit μ_sN. At rest on the slope, f = mg sinθ.
The block holds while mg sinθ ≤ μ_s mg cosθ, which is tanθ ≤ μ_s. The mass cancels. For μ_s = 0.6 the limit is θ = arctan 0.6 ≈ 31.0°.

The at-rest diagram at 2 kg and 25°, to one scale.

m θ

These sliders move the sim too.

The sim accepts the incline diagram with or without friction. Without it, the diagram describes a frictionless slope.

See itDraw all three forces at 25°, then again at 40°, with friction at its limit. Watch for: Net force 0.00 N at 25°, and 3.59 N left down the slope at 40°.

Circular motion depends on the frame

Inertial frame. The orbiting body has one real force: gravity from the central body, mω²r inward. The inward acceleration ω²r is centripetal acceleration. It is the result of that force, not an extra force.
Rotating frame. The body sits still, so the arrows must sum to zero. The diagram adds a centrifugal force mω²r outward. It has no agent: it is a fictitious force that stands in for the frame's own acceleration.
The Coriolis term −2mω × v′ is on the menu but is zero here, because the body is at rest in its own rotating frame (v′ = 0).

The sim's orbit at m = 2 kg, ω = 1.0 rad/s, r = 2 m: mω²r = 4.0 N.

The check grades the orbit against the frame you chose, because the correct diagram differs between them.

See itCheck the orbit in the inertial frame with gravity alone, then in the rotating frame with centrifugal added. Watch for: Net force 4.00 N inward in the inertial frame, and 0.00 N in the rotating frame.

Third-law pairs sit on two diagrams

When A pushes B with a force, B pushes A with an equal and opposite force. The two forces act on different bodies, so each sits on a different diagram and they never cancel.
In the two-body scenario, B's diagram has gravity (Earth), the normal force (floor) and the push from A. B's push on A belongs on A's diagram.
On B, gravity and the normal force cancel, so F_net = F_app and a = F_app/m.
The agent is whatever actually touches the body. In the stacked boxes, the upper box's normal force comes from the lower box, not from the table.

The two-body scenario at F_app = 5 N: the pair acts at the face where A and B touch.

See itDraw B's three forces with F_app = 5 N, then check. Watch for: Net force 5.00 N, a = 2.50 m/s² for m = 2 kg, and B sliding away from A.

Where it matters

Structures. Engineers analyse a bridge truss or a crane by drawing a free-body diagram of each joint or member and requiring the forces on it to sum to zero.
Slopes. Whether a load, a pile of sand or a hillside holds comes down to the same comparison as in section 05: the slope's tangent against the friction coefficient. Dry sand settles at an angle of repose of roughly 30° to 35°.
Centrifuges. In a lab centrifuge, the tube wall pushes a sample inward with mω²r. In the frame of the spinning rotor the sample sits still, and the same force is balanced by a centrifugal term.

Go deeper: the fictitious forces

The rotating-frame terms the sim offers after you declare the frame.

Both terms exist only in the rotating frame. Neither has an agent, and each is proportional to the mass.
The Coriolis term needs a velocity v′ measured in the rotating frame. It is the reason moving air and water curve on a spinning Earth.

Summary

In one line. A free-body diagram has one arrow for each agent acting on the body, and the vector sum of the arrows sets the acceleration through F_net = ma.

Key points

Every arrow needs an agent that you can name.
Balanced arrows mean a = 0. Otherwise a = F_net/m.
On an incline, gravity is vertical, the normal is perpendicular to the surface, and friction is along it, up to μ_sN.
Circular motion: one real force in the inertial frame, plus a fictitious one in the rotating frame.
Third-law partners act on different bodies.

Common mix-ups

"A moving body needs a force in its direction of motion." Constant velocity needs no net force, and "motion" is not an agent.
"Action and reaction cancel, so nothing could accelerate." They act on two different bodies, so they never appear on the same diagram.
"An orbiting body needs an outward force to balance gravity." In the inertial frame the inward pull is unbalanced and gives it ma. Only the rotating frame adds an outward term.

Things to try on your own

In the orbit scenario, double ω and compare the size of the gravity arrow before and after. It scales as ω².
On the two-body scenario, set F_app = 10 N. Work out |a| from F_app and m first, then check against the readout.
On the incline at θ = 40°, draw friction at its limit μ_sN and compare the net force with mg sinθ − μ_sN.