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.”
| Misconception band | Status | Confirmed | Provisional | Clear |
|---|---|---|---|---|
| P1 — Component independence | CLEAR | 10% (2/21) | 14% (3/21) | 76% (16/21) |
| P2 — Projectile acceleration (g down) | CLEAR | 14% (3/21) | 24% (5/21) | 62% (13/21) |
| P3 — Trajectory shape and graph-vs-path | CLEAR | 5% (1/21) | 19% (4/21) | 76% (16/21) |
| P4 — Mass-independence vs drag (provisional-only) | CLEAR | — | 19% (4/21) | 81% (17/21) |
| C-K1 — Circular acceleration to the centre and why | MAJOR | 43% (9/21) | 24% (5/21) | 33% (7/21) |
| C-K2 — Period / angular-to-linear (provisional-only) | CLEAR | — | 24% (5/21) | 76% (16/21) |
| C-D0 — Curving needs inward; release to tangent | CLEAR | 10% (2/21) | 19% (4/21) | 71% (15/21) |
| C-D1 — Net inward force is a role | MAJOR | 52% (11/21) | 24% (5/21) | 24% (5/21) |
| C-D2 — Vertical circle and passive force | WATCHLIST | 14% (3/21) | 43% (9/21) | 43% (9/21) |
| C-D3 — No centrifugal force (inertial frame) | CLEAR | 10% (2/21) | 14% (3/21) | 76% (16/21) |
| C-D4 — Banked curve | MODERATE | 29% (6/21) | 24% (5/21) | 48% (10/21) |
Two MAJOR verdicts, one story. C-D1 (52% confirmed) and C-K1 (43% confirmed) flag together — the expected stack: a class that cannot say why the acceleration points inward treats “centripetal” as a free-floating extra force. The delivered summary sequences the C-K1 change-in-velocity construction first, then the C-D1 arrow-removal drill.
WATCHLIST is not MODERATE. C-D2 shows 43% provisional but only 14% confirmed — a provisional-heavy profile that earns a recheck next cycle, not a remediation block. Keeping settled misconceptions apart from one-off slips is the point of the trichotomy.
Capped bands read differently. P4 and C-K2 show “—” under Confirmed because two-question bands are capped at provisional by design; a strong provisional share there is a prompt to confirm in class, not a verdict.
The strongest verdicts mark the highest-leverage targets. Read the Confirmed column against Provisional to separate settled misconceptions from one-off slips — the WATCHLIST verdict exists precisely for the provisional-heavy case. The cross-cutting acceleration-direction lens is reported as a cohort share, never as a band. Your class receives this readout and the accompanying per-question heatmap, generated from your students' responses and delivered within 48 hours of class completion.
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 25–30 minutes (24 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, Sherwood & Bernard, and Moore. Our physics content has previously been licensed by Cengage.
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. Four sister diagnostics are also available — Motion, Newton's Laws, Energy, and Momentum — same format, same 48-hour turnaround.
View the Motion Diagnostic → View the Newton's Laws Diagnostic → View the Energy Diagnostic → View the Momentum Diagnostic →