Linear momentum is one of the three conservation laws the College Board tests on AP Physics 1, and on the Free Response Question side it is the conservation law that most often costs a candidate a point for what looks like a trivial slip. Students know p = mv, they know momentum is conserved in an isolated system, and they know the impulse–momentum theorem. The reason a 5 still escapes them is that the rubric does not score a sentence that says 'momentum is conserved' — it scores a specific row about the system, a specific row about external forces, a specific row about the vector form, and a specific row about the final values. This article walks through the four rubric rows that a linear-momentum FRQ on AP Physics 1 will almost always demand, and then through the MCQ patterns where momentum gets tested inside a distractor designed to look like an energy problem.
The exam-format snapshot for AP Physics 1 linear momentum
Linear momentum lives in Unit 5: Momentum of the AP Physics 1 course and exam description. It is tested on both sections of the exam: the 80-minute Multiple Choice section (50 questions, 40 of which count) and the 100-minute Free Response section (5 questions). On a typical administration, momentum shows up as one dedicated MCQ cluster, a handful of single questions mixed into other units, and one full FRQ — frequently FRQ 2 or FRQ 3 — whose stimulus is either a 1-D collision diagram, a 2-D explosion-style split, or an impulse-versus-time graph.
For scoring, the multiple choice section contributes 50% of the composite score, and the FRQ section contributes the other 50%. Each FRQ is graded on a 0–10 scale at scoring, then converted to a 1–5 AP grade by a curve that varies slightly year to year. The way to read the rubric on a momentum problem is row by row; the points are not awarded for an overall 'show', they are awarded for distinct, identifiable claims. A candidate who knows the format — that there will typically be a part (a) on defining or identifying the system, a part (b) on setting up the conservation or impulse equation, a part (c) on plugging in values, and a part (d) on a justification or a follow-up comparison — will walk into the prompt already knowing where the rows are going to land.
For the purpose of preparation strategy, this means two things. First, drilling past FRQs by writing out the four rows by hand is more efficient than re-reading the prompt. Second, on the MCQ side, the time budget that matters is the 90-second triage per question: you read the stem, you locate which conservation law or theorem the question is hiding, you make a one-line decision, and you move on. I have watched strong students lose 4–6 minutes on a momentum question trying to decide whether to use energy or momentum, and that decision should be made in under 60 seconds if the stem has been read carefully.
Row 1 — The system row: which objects belong in the closed system
Almost every linear-momentum FRQ on AP Physics 1 begins, implicitly or explicitly, with a row that scores the identification of the system. The rubric rarely gives this row a label, but the readers are trained to look for it: which objects did you include in the system whose momentum you claim is conserved, and which objects did you exclude? The reason this row exists is that momentum conservation is a statement about an isolated system, and the candidate has to demonstrate that the system they chose is, in fact, isolated over the time interval in question.
For a 1-D inelastic collision between two carts on a low-friction track, the system is 'cart A plus cart B'. The rubric wants a sentence or a clear physical statement to that effect. The common failure mode is the student who writes only 'momentum is conserved' without naming the system, and the reader cannot award the point because the claim is not falsifiable from the page. A second failure mode is the student who names the wrong system — for example, treating each cart separately and claiming momentum is conserved in cart A alone. The reader will mark this row wrong even if the algebra downstream is correct, because the foundational identification is missing.
For a 2-D explosion problem, where a single stationary object splits into two pieces, the system is 'piece 1 plus piece 2 plus, if relevant, the original object before the split'. The rubric wants you to assert that the total momentum before the split equals the total momentum after the split, and the pieces after the split are the explicit components. The system row is also where the candidate is expected to acknowledge that the external forces (gravity in the vertical direction, friction, normal force) are either negligible or are internalised correctly within the chosen interval.
For an impulse-style problem, where a force is applied to a single object for a short time, the system is the single object and the rubric row is about the impulse delivered, not about a multi-object conservation. The candidate has to state that the impulse equals the change in momentum of the single object. This is a different row from the conservation row, and confusing the two is one of the highest-frequency losses I see on scored FRQs.
Row 2 — The external-force row: showing why the system is isolated
The second row the rubric reads is the external-force row, and it is the row that distinguishes a 3 from a 5. A student who writes the conservation equation pi = pf without justifying why the system is isolated is gambling on a partial credit row. The reader is specifically trained to look for a sentence that names the external forces acting on the system and a sentence that explains why those external forces are negligible, cancel, or are perpendicular to the motion in question.
The most common way to satisfy this row is to write something like: 'The external forces on the two-cart system are gravity, the normal force from the track, and friction. Gravity and the normal force cancel in the vertical direction. Friction is negligible because the track is low-friction. Therefore, the net external force in the horizontal direction is zero and the horizontal component of momentum is conserved.' That paragraph, written in any competent form, will satisfy the row. The candidate does not need to compute the friction force — they need to name it and dismiss it.
For a 2-D explosion problem, the external-force row often becomes a vertical-momentum row. Before the split, the original object is at rest, so the total momentum is zero. After the split, if one piece flies to the right and the other flies to the left, the horizontal components must cancel. If the problem specifies that the split is in a horizontal plane or that air resistance is negligible, the candidate must say so. The vertical component of momentum remains zero throughout if the motion stays in the horizontal plane; the candidate has to assert this or they lose the row.
A trap on this row is the problem where gravity is not negligible — for example, a ball dropped onto a cart, or a projectile that explodes mid-air. In that case, the external-force row is not 'momentum is conserved' but 'momentum is conserved in the horizontal direction only'. The rubric will only award this row if the candidate restricts the conservation claim to the appropriate component, and the most common loss is a candidate who writes 'momentum is conserved' as an absolute statement and then is marked down for ignoring gravity.
A second trap is the problem where friction is not negligible. The rubric will mark the external-force row wrong if the student claims friction is negligible when the problem stem explicitly says the surface is rough. The candidate's job is to read the friction coefficient, compute the friction force, and either include it on the impulse side of the impulse–momentum theorem or restrict the conservation claim to an interval where friction has not yet had time to act. The rubric reads this row literally.
Row 3 — The vector row: components, signs, and the 'final' justification
The third row is the vector row, and it is where most of the sign losses on the FRQ occur. The rubric wants the candidate to write the conservation (or impulse) equation with explicit vector components, explicit signs, and an explicit identification of which side of the equation is 'before' and which is 'after'. A candidate who writes m1v1 + m2v2 = (m1 + m2)vf without any sign convention loses the row even if the numerical answer is correct, because the reader cannot verify that the candidate understood which direction was positive.
For 1-D problems, the candidate should choose a positive direction (usually to the right, sometimes defined by the motion of one of the objects), state the choice, and assign signs to each velocity accordingly. A common error is to write the equation with one velocity unsigned — for example, leaving a velocity as 3 m/s when it should be −3 m/s — and the reader will mark the vector row wrong because the sign of the contribution to the total momentum is wrong, even if the magnitude is right.
For 2-D problems, the rubric wants the candidate to write the conservation equation in component form, often as two separate equations: one for the x-components and one for the y-components. The x-equation and the y-equation are scored as part of the same vector row. A candidate who writes a single vector equation without breaking it into components may lose half the row, because the reader needs to see that the candidate can handle two independent scalar equations from one vector equation. On the AP Physics 1 exam, 2-D momentum problems almost always have a known 'before' state (often a single object at rest, total momentum zero) and an 'after' state with two pieces moving at angles, and the candidate has to resolve each velocity into x and y components using sine and cosine of the given angles.
The 'final' justification is a sub-row within the vector row, and it is the row that catches the candidate who solves the algebra correctly but does not answer the question. If the prompt asks for the speed of one piece, the candidate must give the speed, not the velocity. If the prompt asks for the direction, the candidate must give an angle, not just a sign. If the prompt asks for the magnitude of the impulse, the candidate must give a positive number with units, not a signed vector. The rubric wants a clean final answer that matches what was asked, and the candidate has to read the question's exact wording to satisfy this sub-row.
Row 4 — The calculation row: units, significant figures, and the 'check' sub-row
The fourth row is the calculation row, and it is more about hygiene than physics. The rubric wants the candidate to substitute numerical values into the equation, carry units through the calculation, and report a final answer with units. The candidate does not have to be exact on significant figures — the College Board accepts two or three significant figures on a typical FRQ — but the answer must be dimensionally consistent. A candidate who reports a speed in kg·m/s has lost the calculation row even if the number is right, because the units are wrong.
A second part of the calculation row is the 'check' sub-row, which is most often scored on the final part of a multi-part FRQ. The candidate is asked to verify the answer by an independent method — for example, by computing the kinetic energy before and after and confirming that the energy is less after an inelastic collision, or by checking that the impulse computed from the area under a force-versus-time graph matches the change in momentum computed from the velocity values. The rubric awards a separate point for this verification, and the candidate has to do the check explicitly. Writing 'the answer seems reasonable' is not a check; the candidate has to do a second calculation and compare it to the first.
On the MCQ side, the calculation row is where the 90-second triage pays off. A momentum MCQ on AP Physics 1 typically gives three to four numerical values and asks for a single number. The candidate who correctly identifies the conservation law and writes the equation with the right signs can solve most momentum MCQs in under 90 seconds. The candidates who take longer are usually the ones who started by trying to use energy, realised mid-calculation that the answer was wrong, and backtracked.
For preparation strategy, the calculation row is best drilled by writing out the four rows by hand for ten past FRQs and timing yourself. After three or four problems, the row structure becomes automatic, and on the exam day the candidate can write the rows without thinking about them. This is the only way I have seen students move from a 3 to a 5 on the momentum FRQ in a single preparation cycle.
MCQ pattern 1 — Conservation disguised as an energy problem
The first MCQ pattern on linear momentum is a problem that gives you velocities, masses, and a 'before' and 'after' state, and the distractors are written in energy units. The question is asking for a momentum quantity, but three of the four answer choices are in joules and one is in kg·m/s. The correct answer is the kg·m/s choice, and the candidate has to recognise the unit mismatch before doing any calculation. This is the kind of question that takes 30 seconds if you read the stem carefully and 4 minutes if you compute kinetic energy for the wrong quantity.
The triage for this pattern is: read the stem, identify the quantity being asked for, check the units of the answer choices, eliminate the joule choices, and solve the momentum equation with the remaining choice(s). On a well-written AP Physics 1 MCQ, this pattern appears at least once per exam, and the candidate who falls for the distractor will lose 2–3 minutes on a question that should take 60 seconds.
MCQ pattern 2 — Impulse-momentum theorem with a graph
The second pattern is an impulse–momentum theorem question, where the stimulus is a force-versus-time graph and the question asks for the change in momentum of an object. The area under the curve is the impulse, and the change in momentum equals the impulse. The distractor choices are usually: the peak force, the duration of the force, the slope of the curve at a specific point, and the correct area. The candidate has to compute the area (often a triangle or a trapezoid) and report the impulse with units of kg·m/s or N·s.
The triage for this pattern is: identify the shape under the curve, compute the area, and report with units. The candidate who tries to read the graph as a position-versus-time graph (a common error from students who have not yet internalised the difference) will compute the wrong quantity and lose the point. The 90-second budget is enough for this pattern if the candidate has practised the area-under-the-curve computation on a few past problems.
MCQ pattern 3 — Two-object collision with a missing value
The third pattern is a two-object collision where the prompt gives you three of the four velocities and masses and asks for the fourth. The conservation equation is m1v1i + m2v2i = m1v1f + m2v2f, and the candidate has to solve for the unknown. The trap is that the unknown is sometimes on the 'before' side, sometimes on the 'after' side, and the candidate has to rearrange the equation accordingly. A second trap is that the problem may give the kinetic energy loss and ask for the unknown velocity, in which case the candidate has to use both the momentum and the energy equations, a combination that is the hardest single calculation on the AP Physics 1 momentum unit.
The triage for this pattern is: write the conservation equation, identify the unknown, solve algebraically before plugging in numbers, and check the sign of the answer against a physical expectation (a cart that was hit from behind should end up moving faster than it started, for example). The candidate who plugs in numbers first and rearranges second will usually get the algebra wrong on the first pass, costing 2–3 minutes per question.
Common pitfalls and how to avoid them
There are four pitfalls that show up on most scored momentum FRQs, and they are worth memorising in their pitfall form. The first is the wrong-system pitfall: the candidate treats one of the two objects as the system and writes 'momentum is conserved' for that object alone. The fix is to write 'system = object 1 + object 2' explicitly at the top of the solution. The second is the uncancelled-external-force pitfall: the candidate writes the conservation equation without addressing friction, gravity, or the normal force. The fix is to add a sentence that names each external force and dismisses it. The third is the sign-convention pitfall: the candidate writes the equation with one velocity unsigned and loses the vector row. The fix is to choose a positive direction and assign a sign to every velocity before writing the equation. The fourth is the unit-mismatch pitfall: the candidate reports a final answer in the wrong units. The fix is to carry units through the calculation and check the units of the final answer against the units of the quantity requested in the prompt.
For most candidates, the most expensive of these four is the uncancelled-external-force pitfall, because it is a one-sentence loss that the candidate does not see when they re-read their own work. In my experience, the candidates who internalise the 'name each external force and dismiss it' sentence are the ones who move from a 3 to a 5, because the sentence is portable across FRQ topics — the same sentence works on energy problems, on Newton's-second-law problems, and on the rotational dynamics problems that are coming in the next exam cycle.
Comparing the four rubric rows across momentum problem types
It is worth putting the four rows side by side for the three problem types a candidate is most likely to see on the AP Physics 1 exam. The table below shows what each row looks like for a 1-D collision, a 2-D explosion, and an impulse-with-graph problem.
| Rubric row | 1-D collision | 2-D explosion | Impulse from F-t graph |
|---|---|---|---|
| System row | Cart A + Cart B | Piece 1 + Piece 2 (after) = original object (before) | Single object receiving the impulse |
| External-force row | Friction negligible, gravity and normal cancel | Vertical momentum conserved only if motion is horizontal; otherwise resolve gravity | Net external force on the object over the interval is the area under the F-t curve |
| Vector row | Choose positive direction, assign signs to all four velocities | Write x-equation and y-equation separately, resolve angles with sine and cosine | Impulse is a vector, but the change in momentum is the area, signed by the direction of the force |
| Calculation row | Substitute, carry units, report final speed or velocity with units | Solve the two-equation system, report magnitudes and angles | Compute the area of the geometric shape under the curve, report impulse in N·s or kg·m/s |
Reading across the table, the system row and the calculation row look similar across all three problem types, but the external-force row and the vector row diverge. A 1-D collision is the easiest of the three on the external-force row, because the candidate usually only has to dismiss friction. A 2-D explosion is the hardest on the vector row, because the candidate has to handle two independent equations. The impulse-with-graph problem is the easiest on the vector row but the hardest on the calculation row, because the candidate has to compute an area rather than a product.
Preparation strategy: a two-week drill plan for the momentum unit
For a candidate who has six to eight weeks before the exam, the momentum unit should be drilled in two passes. In the first pass, work through five to seven past FRQs in timed conditions (12 minutes per FRQ) and grade yourself using the official scoring guidelines. The goal of the first pass is to identify which of the four rows you are losing most often, and to write down the row you are losing in a single sentence. Most candidates will discover they are losing the external-force row and the vector row, in roughly equal proportions.
In the second pass, drill the rows you lost. If you lost the external-force row, write a paragraph for each past FRQ that names every external force on the system and dismisses it. If you lost the vector row, write the conservation equation in component form for each past FRQ, with explicit sign assignments. The second pass should take 4–5 sessions of 30–45 minutes each, and the goal is to internalise the row structure so that you do not have to think about it on exam day.
For the MCQ side, the preparation is faster: 20–30 momentum MCQs in untimed conditions, focused on the three patterns above. The goal is to read each stem carefully, identify the pattern, and solve it in under 90 seconds. If a question takes longer than 2 minutes, mark it, move on, and come back to the marked questions in a second pass. The momentum MCQ section is a place where careless errors are common, and the candidate who has drilled the patterns will read each stem with a clear triage in mind.
The last tactical note is to take at least one full-length FRQ section under timed conditions in the final week before the exam. The FRQ section is 100 minutes for five questions, and the momentum FRQ will typically be one of the five. The candidate who has practised the timing will arrive at the momentum problem with 18–22 minutes left, which is enough to write the four rows without rushing. The candidate who has not practised the timing will arrive with 8–10 minutes left, and the four rows will collapse into a single hurried equation that loses two of the four rows.
Conclusion and next steps
Linear momentum on AP Physics 1 is a conservation law with a specific rubric structure, and the candidates who score 5s are the ones who write the four rows — system, external forces, vector components, calculation — without prompting. The MCQ side rewards pattern recognition and a 90-second triage; the FRQ side rewards the discipline of writing the rows in the order the rubric reads them. For a candidate who is preparing for the next AP Physics 1 administration, the highest-leverage next step is to take three past momentum FRQs, write the four rows for each one, and grade yourself against the official scoring guidelines. AP Courses' one-to-one AP Physics 1 FRQ programme pairs each student with a tutor who scores their four-row write-ups against the rubric and turns the row-by-row pattern into a concrete preparation plan, with the impulse-momentum theorem setup line and the 2-D component write-up as the two highest-priority targets.