Momentum is the topic where conservation language does the most damage — “momentum is conserved” recited as a slogan, detached from the conditions that make it true. A single-sitting diagnostic that maps the exact misconceptions your students carry: what an impulse actually delivers, conservation and the system boundary, reciprocity, signed vector momentum, and elastic versus inelastic collisions. Heatmap delivered within 48 hours of class completion.
A student can compute p = mv, balance a conservation equation, and produce correct answers on familiar problem types — and still believe that joined carts keep their incoming speed, that a bounce destroys momentum, or that equal pushes produce equal speeds regardless of mass. A class can score 70% on a procedural momentum test and 50% on this diagnostic; that gap is the diagnostic finding. These patterns appear across IB, AP, A-Level, and IGCSE classrooms.
A cart already carries 6 kg m/s of momentum and receives a 4 N s impulse along its motion. Asked for the momentum afterward, many students answer 4 kg m/s — the impulse has become the new momentum, and the starting 6 has been dropped. An impulse delivers a change in momentum: the cart ends at 10 kg m/s. Reading impulse as a state rather than a transfer is the foundational momentum misconception — it sits upstream of everything that follows.
A car brakes to a stop. Taking the car alone as the system, many students say its momentum is conserved — “momentum is always conserved” — missing the large external impulse from road friction. Show the same students two baseballs colliding in mid-air and the error flips: “gravity acts, so momentum cannot be conserved.” Both errors skip the actual condition: a chosen system, a stated interval, a negligible net external impulse.
A 1 kg cart at 6 m/s couples to an identical cart at rest. Many students keep the speed at 6 m/s — “because momentum is conserved.” But conserving the momentum — 6 kg m/s, now spread over 2 kg — gives 3 m/s; keeping the speed would double the momentum in the name of conserving it. This is the headline confusion of the collision cluster: momentum read as speed.
The same constant force acts for the same time on a cart of mass m and a cart of mass 2m, both starting from rest. Equal force for equal time means equal impulse and equal momentum change — but the lighter cart ends twice as fast. Students collapse impulse, momentum change, and velocity change into one quantity. The diagnostic tracks this as a cross-cutting compensation lens that fires only when both faces of the error appear together.
The diagnostic surfaces nine scored misconception bands across twenty-four items, plus the L-COMP compensation lens. Coverage spans the conceptual surface of momentum at upper-secondary level — from what an impulse actually delivers, through conservation and the system boundary, conditions for conservation, and reciprocity, to signed vector momentum, two-dimensional conservation, and the collision cluster.
“The new momentum equals the impulse” — dropping the momentum already carried. The force-time area; the same-force-same-time comparison. The instrument's foundational keystone.
Momentum transferred, not destroyed, within a chosen system: the wall bounce, mass-blind recoil from rest, and the internal spring that cannot move the centre of mass.
“Always conserved” and its mirror image: the braking car's large external impulse; gravity's negligible impulse over a brief mid-air collision. Both faces skip the negligible-net-external-impulse condition.
Equal-and-opposite forces and momentum changes with unequal velocity changes: the cannon comparison, and internal-force self-propulsion at the dashboard.
Momentum as a signed vector: the same-speed reversal whose momentum change is about 2 m v, not zero; the sign of the momentum change versus the sign of the kinetic-energy change.
Component-by-component conservation in an off-centre collision; the 90-degree result for an equal-mass elastic collision. A two-item, lower-confidence band.
The collision-cluster keystone: sticking does not destroy momentum; conserved momentum is not conserved speed; momentum yes, kinetic energy no.
Momentum conservation alone is one equation with two unknown final velocities — it constrains a collision but cannot finish it. A two-item, lower-confidence band.
A bounce delivers about twice the impulse of a stop — about m v versus about 2 m v. The tip-the-block comparison. A two-item, lower-confidence band.
Fires only when both faces of the compensation error are selected together — “the bigger mass takes a bigger momentum change” with “equal forces mean equal speeds.” Reported as a cohort percentage, never as a band — and remediated first when it fires.
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.
Momentum Mistake Museum of 20 named traps, Words That Hurt language guide of 17 entries, a 22-item Remediation Worksheet in 10 assignable sections, and a Teacher Answer Key — mapped to the specific misconception bands your class triggered.
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 (20–24) | B (16–19) | C (11–15) | D (0–10) | Band |
|---|---|---|---|---|---|---|---|
| Q01 | Impulse changes momentum, not sets it | 96% | 100% | 100% | 100% | 83% | I1 |
| Q02 | Same force, same time: equal Δp, unequal speed | 56% | 67% | 75% | 38% | 50% | I1 |
| Q03 | Forces on a ball in free flight (impetus probe) | 68% | 100% | 100% | 50% | 33% | I1 |
| Q04 | Impulse as the area under a force-time graph | 52% | 100% | 62% | 62% | 0% | I1 |
| Q05 | Bounce: momentum transferred, not destroyed | 72% | 100% | 88% | 25% | 100% | CS1 |
| Q06 | Recoil from rest | 76% | 100% | 88% | 75% | 50% | CS1 |
| Q07 | Internal spring cannot move the centre of mass | 56% | 100% | 62% | 25% | 67% | CS1 |
| Q08 | Same-speed reversal: a change of about 2 m v | 56% | 100% | 88% | 25% | 33% | V1 |
| Q09 | Momentum is a signed vector | 76% | 100% | 100% | 75% | 33% | V1 |
| Q10 | Sign of Δp versus sign of ΔKE | 60% | 67% | 50% | 88% | 33% | V1 |
| Q11 | What is conserved in a perfectly inelastic collision | 48% | 67% | 75% | 38% | 17% | COL1 |
| Q12 | Sticking does not destroy momentum | 64% | 100% | 75% | 88% | 0% | COL1 |
| Q13 | Conserved momentum is not conserved speed | 44% | 100% | 62% | 12% | 33% | COL1 |
| Q14 | Inelastic: momentum yes, kinetic energy no | 56% | 100% | 88% | 50% | 0% | COL1 |
| Q15 | Cannon: equal and opposite forces, unequal speed | 48% | 100% | 62% | 25% | 33% | N3 |
| Q16 | Internal forces cannot self-propel a system | 80% | 100% | 100% | 75% | 50% | N3 |
| Q17 | Car braking: a non-isolated system | 60% | 100% | 62% | 62% | 33% | CS2 |
| Q18 | Mid-air collision: force versus impulse | 44% | 100% | 38% | 62% | 0% | CS2 |
| Q19 | Two-dimensional collision: conserve components | 60% | 100% | 50% | 75% | 33% | V2 |
| Q20 | The 90-degree equal-mass elastic result | 52% | 67% | 50% | 62% | 33% | V2 |
| Q21 | Momentum alone does not determine a collision | 64% | 100% | 75% | 62% | 33% | COL2 |
| Q22 | What more is needed: elastic vs partly inelastic | 32% | 33% | 50% | 25% | 17% | COL2 |
| Q23 | Clay versus rubber: which delivers more impulse | 52% | 67% | 75% | 25% | 50% | COL3 |
| Q24 | Stop versus bounce: about m v versus about 2 m v | 52% | 100% | 75% | 50% | 0% | COL3 |
Q11–Q14 — Band COL1, the collision-cluster keystone. COL1 reads MAJOR: 13 of 25 submissions (52%) confirm it, with 7 more provisional. The headline item Q13 — the coupling cart whose speed is kept instead of halved — sits at 44% overall and collapses to 12% in Band C. Until momentum and speed are separated, no other collision result can settle.
Q02 + Q15 — the L-COMP compensation lens. 3 of 25 submissions (12%) selected both faces of the compensation error together — “the bigger mass takes a bigger momentum change” with “equal forces mean equal speeds” — firing the cross-family lens. The parent bands I1 and N3 each read WATCHLIST: confirmed in only 2 and 1 submissions, but provisional in 11 and 12 — the wide, single-hit spread the status exists to catch before it consolidates.
Q19–Q24 — the lower-confidence trio. V2, COL2, and COL3 all read MAJOR, mostly through the combined confirmed-plus-provisional route (COL2: 1 confirmed but 17 provisional), and each carries the two-item lower-confidence caveat — directional signals, read item by item rather than as settled band verdicts.
Red cells mark the highest-leverage targets. The governing readout is the per-submission statuses aggregated to cohort verdicts — every band reads MAJOR, WATCHLIST, MODERATE, or CLEAR, and the two-item bands (V2, COL2, COL3) carry a lower-confidence caveat. The L-COMP lens and the two folded threads — the impetus probe (Q03) and the turning-angle distractor (Q10) — are reported as annotations, never as band flags. Your class heatmap is 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 Momentum diagnostic suits classes partway through — or just past — a momentum unit; if you are earlier in the mechanics sequence, we will recommend the right starting point.
→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 Momentum diagnostic is strongest when run after the Newton diagnostic — the reciprocity band applies Newton's third law to momentum exchange, and the collision bands' kinetic-energy half points forward to the Energy diagnostic. It runs cleanly on its own too. Four sister diagnostics are also available — Motion, Newton's Laws, Energy, and Projectile & Circular — same format, same 48-hour turnaround.
View the Motion Diagnostic → View the Newton's Laws Diagnostic → View the Energy Diagnostic → View the Projectile & Circular Diagnostic →