The Field Guide
The Mistake Museum
The book behind these diagnostics — 89 of the predictable ways students misunderstand physics, with the exact wording to drop and the one to use instead.
Two-dimensional motion is where procedural fluency most reliably masks conceptual gaps. A student can resolve components, compute a range, and substitute into v²/R without ever deciding where the acceleration points — the formulas do not ask. A single-sitting diagnostic that maps the exact misconceptions your students carry across projectile motion and circular motion. Heatmap delivered within 48 hours of class completion.
The misconceptions that matter here are directional and structural: an acceleration tilted along the velocity, a force that is not real, an axis chosen out of habit. None of them reliably produces a wrong number on routine problems — and all of them produce wrong physics the moment the situation is unfamiliar: a vertical circle at minimum speed, a banked curve below the design speed, a marble released from a curved tube. These patterns appear across IB, AP, A-Level, and GCSE classrooms.
Release one ball from rest and launch a second horizontally from the same table height at the same instant. Many students answer that the launched ball stays up longer, or that a faster launch changes the fall time. They are letting horizontal motion change the vertical fall. It cannot: the fall is governed by gravity alone, and the two balls land together — and independence is two separate claims, not one self-evident fact.
A stone thrown at an angle reaches the top of its arc. Ask for its acceleration at that instant and many students answer zero — the stone has “stopped rising”, so nothing is happening. Others keep a forward “force of the throw” alive in mid-flight. Once the stone leaves the hand the only force on it is gravity: the acceleration is g, straight down, at every instant — including the apex, where the speed is still nonzero.
Ask the class to draw every force on a puck whirled on a string in a horizontal circle. Three arrows belong — tension, gravity, the normal force. In many diagrams a fourth appears — an extra inward arrow labelled “centripetal force”, beside the tension that is already doing the job. “Centripetal” names a role a real, named force plays, not an extra force — the keystone misconception of circular dynamics.
A car takes a sharp left turn and the passenger is pressed against the right-hand door. Ask what pushed them outward and most students name a centrifugal force. In the ground frame nothing pushes the passenger outward: the passenger continues straight, by inertia, while the car turns left underneath — the door comes across and runs into the passenger, pushing them inward.
The diagnostic surfaces eleven misconception bands across thirty items — the projectile family (P1–P4) sitting on the kinematics surface, and the circular families (C-K, C-D) sitting on forces and momentum — plus a cross-cutting acceleration-direction lens tracked across both. The hardest items leave genuine discrimination above strong procedural performance, so a near-ceiling cohort still produces an informative profile rather than a wall of green.
Horizontal and vertical motion run independently — and independence is two separate claims, not one self-evident fact. Distractors let horizontal motion lengthen or shorten the fall.
In free flight the acceleration is g, straight down, at every instant — including the apex. The turning-point error, the tilted acceleration, and the lingering “force of the throw”.
A height–time graph is not the spatial path, and complementary launch angles give equal range at the same speed.
In vacuum every mass falls with a = g; in air, only object-dependent drag breaks the tie. Includes the deflection probe Arons reports over 40% of physics PhD candidates missed. Provisional-only by design.
At constant speed the velocity still changes direction, so the acceleration is real and points inward — and the reason is kinematic: over a short interval, the change in velocity points to the centre.
Rim speed is circumference over period (v = 2πr/T); angular displacement counts the whole turning history. Provisional-only by design.
With no force, motion is straight along the tangent on release — the curved-tube persistence error, the marble expected to keep curving after it exits.
A real, named force — or a component of one — supplies the inward net force; “centripetal” names the role it plays, not an extra force. The fourth arrow; “only a pull can be centripetal”.
A passive contact force cannot pull: a negative normal force means loss of contact, and at the minimum top speed gravity alone supplies the inward force.
In the ground frame there is no outward force: the passenger continues straight by inertia and the door pushes inward — and the third-law partner of the inward pull acts on the string, not on the object.
Take one axis horizontal toward the centre — the net-force direction; below the design speed, static friction acts up the slope; and the banking angle is mass-independent.
One spine misconception — acceleration points where you're going — tracked across both families. Reported only when it shows in both the projectile and circular contexts, and remediated first when it fires, because it sits upstream of projectile acceleration and all of circular dynamics.
Within 48 hours of your class completing the diagnostic, we send you a complete misconception analysis — actionable, teacher-readable, and ready to use in your next lesson.
Colour-coded class heatmap showing performance by question and by student performance band (A–D). Items grouped by misconception band so cluster patterns become visible at a glance.
Teacher-readable summary: which misconception bands hit hardest, what they mean, and how your class distributes across performance bands.
Mistake Museum, Words That Hurt language guide, a sectioned Remediation Worksheet (eleven band sections plus a cross-cutting spine section), and a Teacher Key — keyed to the bands your class actually flagged.
What each performance band (A–D) means for your students, with specific teacher action items — from “structurally sound” to “needs foundational rebuilding.”
| Q# | Concept Tested | Overall | A (25–30) | B (19–24) | C (13–18) | D (0–12) | Band |
|---|---|---|---|---|---|---|---|
| Q01 | Dropped vs horizontal launch | 64% | 50% | 86% | 56% | 60% | P1 |
| Q02 | Which experiment shows which | 28% | 50% | 43% | 22% | 0% | P1 |
| Q03 | Components don’t trade | 56% | 100% | 71% | 44% | 20% | P1 |
| Q04 | Apex acceleration and speed | 56% | 100% | 71% | 56% | 0% | P2 |
| Q05 | Mid-flight acceleration direction | 40% | 75% | 57% | 33% | 0% | P2 |
| Q06 | Forces on a flying stone | 56% | 75% | 57% | 67% | 20% | P2 |
| Q07 | Acceleration arrows along arc | 68% | 100% | 86% | 56% | 40% | P2 |
| Q08 | Complementary angles, equal range | 60% | 75% | 86% | 44% | 40% | P3 |
| Q09 | Height-vs-time graph is not path | 48% | 100% | 57% | 33% | 20% | P3 |
| Q10 | Vacuum vs air: ball and feather | 64% | 100% | 86% | 67% | 0% | P4 |
| Q11 | Electron-beam deflection | 48% | 100% | 57% | 44% | 0% | P4 |
| Q12 | Constant-speed accel direction | 64% | 100% | 71% | 67% | 20% | C-K1 |
| Q13 | Why acceleration points inward | 56% | 100% | 57% | 44% | 40% | C-K1 |
| Q14 | Speeding up: radial + tangential | 56% | 75% | 43% | 67% | 40% | C-K1 |
| Q15 | Rim speed from period | 56% | 100% | 57% | 67% | 0% | C-K2 |
| Q16 | Angle past one full turn | 44% | 100% | 71% | 22% | 0% | C-K2 |
| Q17 | Marble leaving a C-tube | 48% | 75% | 86% | 22% | 20% | C-D0 |
| Q18 | Push to turn a puck | 56% | 100% | 57% | 67% | 0% | C-D0 |
| Q19 | Which force turns the plane | 56% | 100% | 71% | 56% | 0% | C-D1 |
| Q20 | Rate of change of momentum | 36% | 100% | 29% | 33% | 0% | C-D1 |
| Q21 | Rotor: push or pull inward | 36% | 75% | 43% | 33% | 0% | C-D1 |
| Q22 | Centripetal-force arrow error | 52% | 75% | 71% | 56% | 0% | C-D1 |
| Q23 | Tension top vs bottom | 52% | 100% | 71% | 44% | 0% | C-D2 |
| Q24 | Negative normal force at top | 52% | 100% | 71% | 33% | 20% | C-D2 |
| Q25 | Min top speed in a bucket | 48% | 100% | 86% | 22% | 0% | C-D2 |
| Q26 | Pressed to door in left turn | 32% | 50% | 14% | 56% | 0% | C-D3 |
| Q27 | Whirled ball: pull vs centrifugal | 56% | 100% | 86% | 33% | 20% | C-D3 |
| Q28 | Axis choice on banked curve | 44% | 100% | 57% | 22% | 20% | C-D4 |
| Q29 | Friction below design speed | 52% | 50% | 86% | 56% | 0% | C-D4 |
| Q30 | Banking angle, mass-independence | 56% | 75% | 86% | 44% | 20% | C-D4 |
Q02 — Band P1. The component-independence probe is the lowest cell in the table at 28% — and only 50% even in Band A, 22% in C, 0% in D. The kind of item a strong procedural class still misses: telling which experiment demonstrates which claim.
Read across the bins, not just the Overall column. Several items look healthy on average yet crater for the lower scorers — minimum-top-speed (Q25) reads 48% overall but 22% in C and 0% in D. The class average hides where a misconception is concentrated; the A–D split is what surfaces it.
Red cells mark the highest-leverage targets. Compare the Overall column against Bands C and D to find misconceptions hiding behind class averages. Two-question bands are read as lower-confidence signals, and unanswered items are reported as incomplete, not as evidence of understanding.
I carried out a pilot test of the Physics Misconceptions Diagnostics with my Grade 11 (lower 6th) International Baccalaureate classes, as part of their revision for end of year exams. The tests covered Motion Foundations, Forces and Free-Body Diagrams - topics that are fundamental to the IB course as well as A’ level courses.
The tests were all set up by FundaFirst - all I had to do was point the students to web links. The students found the questions easy to access and to carry out. The information that came back from FundaFirst was incredibly useful, identifying areas where the class and/or individuals were weaker. These areas would have been much harder to identify without the tests. FundaFirst then provided concrete examples of how to address the misconceptions, with work sheets targeting these areas.
I will not hesitate to use FundaFirst’s diagnostic testing with future cohorts!
Fill in the form below. The Projectile & Circular diagnostic suits classes finishing or revising projectile motion and circular motion — the two-dimensional block that sits across kinematics and forces.
→You receive a class-specific diagnostic link and a short setup message you can paste directly to your students. No student logins needed.
→Share the link. The diagnostic takes about 32–36 minutes (30 questions, no calculator required, single sitting). In-class or take-home.
→Class heatmap, cohort summary, band profiles, and remediation toolkit emailed to you within 48 hours of class completion.
Share your details below and we'll set up the diagnostic link within 24 hours. No commitment — this is a free pilot designed for teacher use and classroom feedback.
The diagnostic is grounded in physics education research, including the work of Arons, Knight, Chabay & Sherwood, and Moore. A FundaFirst video on the early history of atomic theory was licensed by National Geographic Learning (Cengage) for a chemistry title.
The Projectile & Circular diagnostic is strongest when run after the FundaFirst Motion and Newton diagnostics — the projectile bands sit on the kinematics surface the Motion diagnostics map, and the circular-dynamics bands apply the force concepts the Newton modules diagnose. It runs cleanly on its own too. Eight sister diagnostics are also available — Motion, Newton's Laws, Energy, Momentum, and Oscillations & Waves, Static Electricity, Electric Fields, and Electric Potential — same format, same 48-hour turnaround.
View the Motion Diagnostic → View the Newton's Laws Diagnostic → View the Energy Diagnostic → View the Momentum Diagnostic → View the Oscillations & Waves Diagnostic → View the Static Electricity Diagnostic → View the Electric Fields Diagnostic → View the Electric Potential Diagnostic →
The book behind these diagnostics — 89 of the predictable ways students misunderstand physics, with the exact wording to drop and the one to use instead.