A field guide to being wrong
The Error Atlas
66 recurring reasoning mistakes. For each one: what it looks like, why it feels right, how to catch it, and the physics that fixes it. Your diagnostic report links straight here.
▣ Featured entries
mechanics illustrated
Constant speed is not zero acceleration
detect · You set a = 0 for something moving in a curved path at steady speed.
mechanics illustrated
Static friction is not always at its maximum
detect · You wrote f = μs·N for a body that isn't on the verge of slipping.
mechanics illustrated
Centripetal acceleration points inward
detect · Your free-body diagram has a net outward arrow for something moving in a circle.
≡ Full index
63 of 66 entries
Mechanics 16
NL-01 A free-body diagram shows real forces only Adding a phantom “force of motion” in the direction of travel. Constraint missed NL-03 Zero velocity is not zero acceleration Concluding a = 0 at the instant an object is momentarily at rest. Force / acceleration confusion NL-06 Internal tension needs the right system choice Trying to find an internal force by writing ΣF for the whole system. Constraint missed NL-07 The normal force is not always mg Setting N = mg on an incline, in an elevator, or under an applied force. False equilibrium assumption ▣ NL-08 Third-law pairs act on different bodies Cancelling an action–reaction pair on a single free-body diagram. Force / acceleration confusion NL-09 Mass and weight are different quantities Using kilograms as a force, or reporting weight in kg. Dimensional inconsistency NL-10 Axes are bookkeeping, not physics Thinking a tilted coordinate system changes which forces are real. Vector / scalar confusion NL-11 Tension is uniform only in the ideal string limit Assuming every connected segment has the same tension even with mass or friction in the connector. Constraint missed NL-12 Kinetic friction opposes relative slipping Drawing friction opposite the object's ground-frame velocity instead of opposite slipping at the contact. Force / acceleration confusion NL-13 Constraint equations need signed directions Using equal acceleration magnitudes where the constraint requires opposite signed accelerations. Sign convention error NL-14 Apparent weight is the normal force Treating scale reading and gravitational weight as always identical. False equilibrium assumption NL-15 A spring force depends on displacement from equilibrium Using F = kx without defining x from the spring's relaxed length or equilibrium point. Force / acceleration confusion NL-16 Terminal velocity means zero acceleration, not zero forces Assuming a falling object at terminal speed has no forces acting. Force / acceleration confusion NL-17 The center of mass ignores internal forces Trying to change a system's center-of-mass motion using only internal pushes. Constraint missed NL-18 Banked-curve friction direction depends on speed Assuming friction always points up or down a banked curve regardless of speed. Circular-motion direction error NL-19 Projectile components are independent only after forces are split Letting horizontal velocity affect vertical acceleration in ideal projectile motion. Vector / scalar confusion Rotation 10
ROT-01 Equilibrium needs Στ = 0, not just ΣF = 0 Balancing forces but forgetting the torque condition. Rotation / torque-arm error ROT-02 Torque uses the perpendicular lever arm Writing τ = F·r regardless of the force's direction. Rotation / torque-arm error ▣ ROT-03 Moment of inertia depends on the axis Treating I as a fixed property of the object. Rotation / torque-arm error ROT-04 Rolling without slipping links v and ω Treating translation and rotation as independent while rolling. Constraint missed ROT-05 Angular momentum needs a no-external-torque axis Conserving angular momentum about an axis with a nonzero external torque. Wrong conservation law ROT-06 Static friction can cause rolling without doing work Assuming any friction force always removes mechanical energy. Wrong conservation law ROT-07 Torque sign follows your rotation convention Flipping torque signs because a force points down or left, rather than because of its rotational tendency. Sign convention error ROT-08 Angular acceleration follows net torque, not angular velocity Assuming a spinning object must have a net torque because ω is nonzero. Force / acceleration confusion ROT-09 Radius and diameter are not interchangeable Using diameter where a rolling or torque relation requires radius. Dimensional inconsistency ROT-10 The parallel-axis theorem adds Md² Adding Md or shifting moment of inertia by a linear distance. Dimensional inconsistency Energy 11
EN-01 Energy conservation fails when external work is hidden Applying KE + PE = const when friction, drag, or a motor is present. Wrong conservation law ▣ EN-02 The normal force usually does no work Counting the normal force in the work–energy budget. Wrong conservation law ▣ EN-03 Kinetic energy is a scalar — it has no direction Assigning a direction to KE or adding energies as vectors. Vector / scalar confusion EN-04 Work is path-dependent only with friction Assuming gravitational work depends on the route taken. Path vs. state confusion EN-05 Power is not the same as energy Using watts and joules interchangeably. Dimensional inconsistency EN-06 Spring energy uses displacement squared Using kx or mgx as spring energy instead of ½kx². Dimensional inconsistency EN-07 Friction work depends on path length Treating friction like gravity and using only vertical height change. Path vs. state confusion EN-08 Potential energy needs a reference level Treating gravitational potential energy as an absolute number instead of a difference. Path vs. state confusion EN-09 Work-energy uses net work Equating the work by one force to ΔK while ignoring other forces that also do work. Wrong conservation law EN-10 Energy diagrams need every storage mode Calling energy 'lost' instead of moving it into thermal, spring, rotational, or internal storage. Wrong conservation law EN-11 Bound orbits have negative total energy Assuming a satellite in orbit has positive total mechanical energy because it is moving. Energy vs. momentum misuse Momentum 9
MOM-01 Momentum is conserved only when external impulse is negligible Applying conservation of momentum with a large external force present. Wrong conservation law MOM-02 Energy and momentum are not interchangeable Conserving kinetic energy in an inelastic collision (or momentum via energy). Energy vs. momentum misuse MOM-03 Impulse is a vector — signs matter Computing Δp with speeds instead of signed velocities. Sign convention error MOM-04 Choose the system before applying conservation Applying conservation without defining what's inside the system. Constraint missed MOM-05 Center-of-mass velocity is the system momentum divided by total mass Averaging speeds without weighting by mass. Constraint missed MOM-06 Explosions conserve momentum while kinetic energy can increase Assuming an explosion violates momentum conservation because pieces fly apart. Energy vs. momentum misuse MOM-07 Momentum components conserve separately Conserving the speed-like magnitude of momentum instead of x and y components. Vector / scalar confusion MOM-08 Impulse is area under force-time, not peak force Using the maximum force in a collision as if it were the impulse. Dimensional inconsistency MOM-09 A ballistic pendulum needs two separate models Using momentum conservation through the entire swing, or energy conservation through the collision. Energy vs. momentum misuse Circuits 8
CIR-01 Series and parallel don't combine by 'adding up' Adding resistances in parallel (or reciprocals in series). Circuit equivalence error ▣ CIR-02 Ideal meters: ammeter 0 Ω, voltmeter ∞ Ω Placing meters without accounting for their ideal resistance. Circuit equivalence error CIR-03 Electric potential is not electric field Using V and E interchangeably, or assuming E = 0 wherever V = 0. Dimensional inconsistency CIR-04 Kirchhoff loop signs follow your traversal Changing voltage signs based on how a battery or resistor looks, not on the chosen loop direction. Sign convention error CIR-05 Current is not used up Assuming less current remains after each resistor in a series loop. Circuit equivalence error CIR-06 Series shares current; parallel shares voltage Applying the series current rule to parallel branches or the parallel voltage rule to series elements. Circuit equivalence error CIR-07 A charged capacitor blocks steady DC Treating a capacitor as a wire after a long time in a DC circuit. Circuit equivalence error CIR-08 Changing equivalent resistance changes the source current Adding a parallel branch but keeping total current fixed. Circuit equivalence error Waves & SHM 5
SHM-01 SHM needs a linear restoring force Calling any back-and-forth motion simple harmonic. Force / acceleration confusion SHM-02 Wave speed is set by the medium, not the source Assuming shaking a rope faster makes the wave travel faster. Dimensional inconsistency SHM-03 In SHM, velocity and acceleration peak a quarter-cycle apart Assuming a mass on a spring is fastest where its acceleration is greatest. Force / acceleration confusion ▣ SHM-04 Mass-spring period does not depend on amplitude Assuming a larger oscillation must take longer because it travels farther. Force / acceleration confusion SHM-05 Phase is not the same as path distance Confusing where an oscillator is in its cycle with how far it has traveled. Path vs. state confusion Thermo 4
TH-01 Temperature is not heat Treating a hotter object as necessarily containing more heat. Dimensional inconsistency TH-02 Heat added is not all converted to work Assuming an engine turns all input heat into useful work. Wrong conservation law TH-03 Adiabatic means no heat transfer, not constant temperature Treating Q = 0 as if ΔT = 0. Wrong conservation law TH-04 PV-work sign depends on the convention Mixing work done by the gas with work done on the gas in the same first-law equation. Sign convention error Research basis
Where the taxonomy comes from.
The Atlas follows the physics-education-research tradition of treating a wrong answer as evidence of a specific alternative model, not carelessness. Several categories map to documented results:
- The phantom “force of motion” (NL-01) and impetus-style reasoningClement, Am. J. Phys. 50 (1982) · Halloun & Hestenes, Am. J. Phys. 53 (1985) · McCloskey, Scientific American 248 (1983)
- Velocity / acceleration confusion (the force–acceleration category)Trowbridge & McDermott, Am. J. Phys. 48 (1980) & 49 (1981)
- Distractors authored to detect specific misconceptions — the instrument design this diagnostic imitatesHestenes, Wells & Swackhamer, “Force Concept Inventory,” The Physics Teacher 30 (1992)
- Novices sorting problems by surface features instead of governing principles — why the ladder re-tests one principle in changing costumesChi, Feltovich & Glaser, Cognitive Science 5 (1981)
The entries, codes, and problems here are original. The method — coded distractors, named misconceptions, targeted repair — stands on this literature.