Diagnostic · Impulse & collisions
Momentum Diagnostic
Maps what impulse, conservation and the system boundary mean to your students, including the compensation lens, and shows which band to address first.
IB DP · AP · A-Level · GCSE / IGCSE
1
Forms
24
Questions
25–30
Minutes
9 + lens
Bands
FundaFirst HS diagnostics have run in classrooms at 10 schools · 9 countries · 3 continents
The wrong ideas come from physics education research, which has recorded them since the 1970s: Viennot, Trowbridge & McDermott, Arons, Hestenes, Maloney. The physics comes from Arons, Knight, Moore, and Chabay & Sherwood.
What it maps
Nine misconception bands plus one cross-cutting lens.
I1
Impulse Delivers a Change
The new momentum taken to equal the impulse, with the momentum already carried dropped. The force-time area. The same-force, same-time comparison. Most of the other bands rest on this one.
CS1
Conservation, Transfer & the System Boundary
Momentum moves between objects inside a chosen system and is never destroyed. The wall bounce, recoil from rest whatever the masses, and the internal spring that cannot move the centre of mass.
CS2
Conditions for Conservation
Always conserved, and its mirror image. The braking car has a large external impulse. Gravity gives a small impulse over a brief mid-air collision. Both answers skip the condition on the net external impulse.
N3
Reciprocity
Equal and opposite forces and changes in momentum, with unequal changes in velocity. The cannon comparison, and pushing on the dashboard from inside the car.
V1
Vector Momentum & Sign
Momentum as a signed vector. A reversal at the same speed changes the momentum by about 2 m v, and not by zero. The sign of the change in momentum against the sign of the change in kinetic energy.
V2
Two-Dimensional Conservation
Conservation applied to each component in an off-centre collision, and the 90 degree result for an equal-mass elastic collision. Two items, so a lower-confidence band.
COL1
Elastic and Inelastic: What Is Conserved
The core of the collision cluster. Sticking does not destroy momentum. Conserved momentum is not conserved speed. Momentum is conserved and kinetic energy is not.
COL2
Underdetermined Collisions
Momentum conservation on its own is one equation with two unknown final velocities. It limits a collision but cannot finish it. Two items, so a lower-confidence band.
COL3
Clay vs Rubber
A bounce delivers about twice the impulse of a stop, about 2 m v against about m v. The tip-the-block comparison. Two items, so a lower-confidence band.
L-COMP
The Compensation Lens
Fires only when both faces of the compensation error are chosen together. The two faces are that the bigger mass takes the bigger change in momentum, and that equal forces mean equal speeds. Reported as a percentage of the class and never as a band. When it fires, it is treated first.
A question from it
Students can recite that momentum is conserved and still hold these ideas.
The push becomes the momentum
A cart already has 6 kg m/s of momentum and receives a 4 N s impulse along its motion. Asked for the momentum afterwards, 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, so the cart ends at 10 kg m/s. Most of the other momentum misconceptions grow from this one.
Always conserved, and its mirror image
A car brakes to a stop. Taking the car alone as the system, many students say its momentum is conserved, because momentum is always conserved. They have missed the large external impulse from the road. Show the same students two baseballs colliding in mid-air and the error flips: gravity acts, so momentum cannot be conserved. Both answers skip the real condition, a small net external impulse over the chosen interval.
Conserved momentum, unchanged speed
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. Conserving the momentum of 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 main confusion in the collision cluster, where momentum is read as speed.
Same push, so same speed
The same force acts for the same time on a cart of mass m and a cart of mass 2m, both from rest. Equal force for equal time means equal impulse and equal change in momentum, yet the lighter cart ends twice as fast. Students fold impulse, momentum change and velocity change into one quantity. A lens tracks this, and fires when both faces of the error appear.
How it runs
Students use one shared link and need no logins.
24 questions, about 25–30 minutes, no calculator required, single sitting.
The report arrives within 48 hours of your class finishing.
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Arons and Knight document the misconceptions. Moore and Chabay & Sherwood supply the physics treatment.