AP Physics C: Mechanics Unit 4 Review: Linear Momentum

Q: What's on the AP Physics Mech Unit 4 progress check (MCQ and FRQ)?

The AP Physics C: Mechanics Unit 4 progress check in AP Classroom includes both MCQ and FRQ parts drawn from all four unit topics: Linear Momentum, Change in Momentum and Impulse, Conservation of Linear Momentum, and Elastic and Inelastic Collisions. The MCQ section tests conceptual understanding and calculation, while the FRQ part asks you to set up and solve multi-step problems involving impulse-momentum and collision scenarios. For the progress check, focus on applying the impulse-momentum theorem correctly and distinguishing elastic from inelastic collisions. You can find matched practice problems at AP Physics C: Mechanics Unit 4 .

Q: How do I practice AP Physics Mech Unit 4 FRQs?

Unit 4 FRQs in AP Physics C: Mechanics most often come from Conservation of Linear Momentum and Elastic and Inelastic Collisions, so those two topics should anchor your free-response practice. A typical FRQ will ask you to define a system, justify why momentum is conserved, set up conservation equations, and solve for an unknown velocity or energy loss. To practice effectively: - Write out your system definition and conservation statement before calculating - Show all vector directions explicitly, since momentum is a vector quantity - Practice both perfectly inelastic and elastic collision setups, as each has a different equation structure - Check your work by verifying units and the reasonableness of your answer Find FRQ-style practice problems at AP Physics C: Mechanics Unit 4 .

Q: Where can I find AP Physics Mech Unit 4 practice questions?

The best place to find AP Physics C: Mechanics Unit 4 practice questions, including multiple-choice and practice test problems, is AP Physics C: Mechanics Unit 4 . That page has resources covering all four topics: Linear Momentum, Change in Momentum and Impulse, Conservation of Linear Momentum, and Elastic and Inelastic Collisions. For MCQ practice, look for questions that ask you to calculate impulse, compare momentum before and after a collision, or identify whether kinetic energy is conserved. These are the most common question formats for this unit on the actual exam.

Q: How should I study AP Physics Mech Unit 4?

Start with the impulse-momentum theorem in Topic 4.2 before moving to conservation laws, since understanding how force and time change momentum makes Topic 4.3 much more intuitive. Unit 4 rewards students who practice setting up problems systematically rather than jumping straight to equations. A solid study plan for this unit: 1. **Build the foundation first.** Make sure you can define momentum as a vector and apply p = mv in multiple dimensions before tackling collisions. 2. **Master the impulse-momentum theorem.** Practice interpreting force-time graphs and calculating impulse from area under the curve. 3. **Drill conservation of momentum.** Write out system definitions and justify conservation conditions every time, not just when the problem asks you to. 4. **Separate collision types clearly.** Know that elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve only momentum. 5. **Do timed FRQ practice.** Since this unit is 10-20% of the exam, free-response problems here are high value. All four topics are organized at AP Physics C: Mechanics Unit 4 .

10–20% of AP multiple choice
4 topics
AP exam review verified for 2027

Unit 4 is about how objects exchange momentum during interactions. You learn to define momentum, calculate impulse as an integral of force over time, apply conservation of momentum to collisions and explosions, and classify collisions by what happens to kinetic energy.

Fiveable's AP Physics C: Mechanics Unit 4 review covers 4 topics, with guided practice questions for the unit.

start with 4.1 start unit practiceReview with a tutorFree, 24/7, real people, from UPchieve

AP Physics C: Mechanics unit 4 topics

4.1

Linear Momentum

Defines momentum as p = mv, establishes it as a vector quantity, and introduces the collision and explosion models for analyzing interactions by comparing initial and final system states.

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4.2

Change in Momentum and Impulse

Derives impulse as the integral of net force over time and connects it to change in momentum through the impulse-momentum theorem. Covers graphical interpretation of force-time and momentum-time graphs.

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4.3

Conservation of Linear Momentum

Establishes that total momentum is constant in isolated systems, introduces center-of-mass velocity, and applies conservation component-wise to 1D and 2D collisions and explosions.

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4.4

Elastic and Inelastic Collisions

Classifies collisions by kinetic energy behavior: elastic (KE conserved), inelastic (KE decreases), and perfectly inelastic (objects stick). Momentum is conserved in all cases.

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Practice AP Physics C: Mechanics unit 4 questions

Try AP-style questions on unit 4, then use the review notes below for anything you miss.

Example AP-style MCQs

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MCQ

AP-style practice question

Question

A 0.50 kg ball strikes a wall horizontally at 10 m/s and rebounds in the opposite direction at 8.0 m/s. The contact lasts 0.10 s. A student claims the average force exerted by the wall has a magnitude of 90 N. Which of the following correctly evaluates this claim with appropriate justification?

Incorrect, because the scalar speed change is 2.0 m/s, requiring an impulse of 1.0 N·s to slow the ball's motion.

Incorrect, because the kinetic energy change is 9.0 J, requiring an impulse of 90 N·s to account for energy loss.

Correct, because the vector velocity change is 18 m/s, requiring an impulse of 9.0 N·s to reverse the ball's direction.

Correct, because the sum of initial and final forces is 90 N, which represents the average interaction strength.

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MCQ

AP-style practice question

Question

Object A of mass $m$ moves at speed $v$ and collides with identical Object B at rest. They scatter at $45^\circ$ angles to the original direction with equal speeds. A student claims the collision is elastic. Which reasoning supports this?

Correct, because the objects separate after impact rather than sticking together to move with a common final velocity.

Incorrect, because the vector sum of final velocities is less than the initial velocity due to the scattering angles.

Incorrect, because momentum is conserved in the x-direction but kinetic energy is lost to the y-direction components.

Correct, because the final total kinetic energy equals the initial kinetic energy based on the scattering geometry.

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Example FRQs

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FRQ

Elastic versus inelastic collision determination

1. A ball of mass m approaches a vertical wall along a horizontal frictionless surface, as shown in Figure 1. The ball is moving in the +x-direction with speed v0 when it collides with the wall at time t = 0. The collision lasts until time t = T. During the collision, the wall exerts a horizontal force on the ball that varies with time according to F(t) = Fmax*sin(πt/T), where Fmax is the maximum magnitude of the force exerted by the wall on the ball. After the collision, the ball moves in the -x-direction.

Figure 1: Ball of mass m moving toward a rigid vertical wall on a frictionless horizontal surface (positive x to the right).

Figure 2: Momentum vector diagrams for the ball before and after the collision (vertical sign convention: up is positive momentum, down is negative momentum).

The diagrams in Figure 2 can be used to represent the momentum of the ball before and after the collision. The momentum vector diagram for the ball before the collision is shown.

Draw an arrow on the right grid to represent the momentum vector of the ball after the collision.

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The arrow should start at the zero-momentum line.

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The length of the arrow should be proportional to the relative magnitude compared to the momentum before the collision.

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The direction of the arrow should represent the sign of the momentum (positive upward, negative downward).

ii.

During the time interval 0 <= t <= T, the wall exerts a force F on the ball along the x-direction as a function of t that is modeled by F(t) = Fmax*sin(πt/T), where Fmax is the maximum magnitude of the force exerted by the wall on the ball during the collision.

Derive an expression for Fmax in terms of m, v0, vf, T, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Describe a procedure to experimentally determine whether the collision is elastic or inelastic. Your description should include: Consider whether the collision between the ball and the wall is elastic or inelastic. In an elastic collision, kinetic energy is conserved. In an inelastic collision, kinetic energy is not conserved.

What quantities should be measured
How these measurements would be used to make the determination
What specific criterion distinguishes an elastic collision from an inelastic collision

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FRQ

Elastic collision between two carts momentum conservation

4. Two carts, cart A of mass 2 (see Figure 2) (see Figure 3).0 kg and cart B of mass 3.0 kg, are on a horizontal frictionless track. Cart A moves to the right with an initial speed of 4.0 m/s toward cart B, which is initially at rest, as shown in Figure 1. The carts collide.

Figure 1: Before collision (initial conditions on a frictionless horizontal track)

Figure 2: After elastic collision (Scenario 1)

Figure 3: After perfectly inelastic collision (Scenario 2)

During the collision in Scenario 1, the magnitude of the impulse delivered to cart A by cart B is $J_A$ , and the magnitude of the impulse delivered to cart B by cart A is $J_B$ .

Indicate whether $J_A$ is greater than, less than, or equal to $J_B$ by writing one of the following.

$J_A > J_B$
$J_A < J_B$
$J_A = J_B$

Justify your answer using qualitative reasoning beyond referencing equations.

Derive an expression for the final velocity $v_{B,f}$ of cart B after the elastic collision. Express your answer in terms of $m_A$ , $m_B$ , $v_{A,i}$ , $v_{A,f}$ , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Consider the elastic collision in Scenario 1, where cart A has mass $m_A$ and initial velocity $v_{A,i}$ , and cart B has mass $m_B$ and is initially at rest. After the collision, cart A has final velocity $v_{A,f}$ .

Indicate whether $\Delta p_{A,1}$ is greater than, less than, or equal to $\Delta p_{A,2}$ . Compare the magnitude of the change in momentum of cart A in Scenario 1 (elastic collision) to the magnitude of the change in momentum of cart A in Scenario 2 (perfectly inelastic collision). Let $\Delta p_{A,1}$ represent the magnitude of the change in momentum of cart A in Scenario 1, and let $\Delta p_{A,2}$ represent the magnitude of the change in momentum of cart A in Scenario 2.

Briefly justify your answer.

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FRQ

Collision coefficient of restitution determination

3. A student is given two carts, Cart A of mass mA = 0.50 kg and Cart B of mass mB = 1.0 kg, on a horizontal track. Cart A is initially moving with speed v0 toward Cart B, which is initially at rest.

Students are asked to experimentally determine the coefficient of restitution e for collisions between the two carts using a linear graph. To determine e, the students are permitted to use measurements from only the motion sensor and the meterstick.

Describe an experimental procedure using the described setup to collect data that would allow the students to determine an experimental value of e using a linear graph. Include any steps necessary to reduce experimental uncertainty. In your description, state what quantities would be measured and how the measurements would be made.

Describe how the data collected in part A could be graphed and how that graph would be analyzed to determine the value of e. Include which quantities should be graphed on each axis and how the coefficient of restitution e relates to features of the graph.

Figure 1. Initial setup before collision

Figure 2. After collision

Figure 3. Blank grid for plotting data

vAi (m/s)	vAf (m/s)	vBf (m/s)
0.80	-0.12	0.46
1.20	-0.18	0.69
1.60	-0.24	0.92
2.00	-0.30	1.15
2.40	-0.36	1.38

The student performs the experiment by giving Cart A various initial speeds vAi while Cart B remains at rest (vBi = 0). For each trial, the student measures the initial speed of Cart A and the final speeds of both carts after the collision. The student's measurements are shown in Table 1.

Indicate two quantities, either measured quantities from Table 1 or additional calculated quantities, that could be graphed to produce a straight line that could be used to determine e.

Vertical axis: Horizontal axis:

ii.

On the grid provided in Figure 3, create a graph of the quantities indicated in part C(i).

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Use Table 2 to record the measured or calculated quantities that you will plot.

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Clearly label the axes, including units as appropriate.

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Plot the points you recorded in Table 2.

iii.

Draw a best-fit line to the data graphed in part C(ii).

Using the best-fit line that you drew in part C(iii), calculate an experimental value for the coefficient of restitution e. Show your work clearly.

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AP Physics C: Mechanics unit 4 practice test

A timed, AP-style test built only from unit 4 questions — multiple choice plus free response, scored with AI feedback. Use the standard format or build your own.

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Unit 4 review notes

4.1

Linear Momentum

Linear momentum is defined as p = mv. Because velocity is a vector, momentum has both magnitude and direction. For a system of objects, total momentum is the vector sum of individual momenta. Collisions and explosions are modeled by comparing the system's momentum just before and just after the interaction, treating each object as a point mass.

p = mv: Linear momentum equals mass times velocity; direction matches the direction of velocity.
Vector addition: System momentum is the sum of all individual momenta, requiring component-wise addition in 2D problems.
Collision model: Internal forces during the interaction are much larger than external forces, so only initial and final states need to be analyzed.
Explosion model: Internal forces push system objects apart; total momentum before and after is still compared using the same framework.
Object model: Each object is treated as a point mass during a collision, ignoring size and internal structure.

If a 2 kg object moves at 3 m/s east and a 1 kg object moves at 6 m/s west, what is the total momentum of the system?

Interaction type	Internal forces	Objects after
Collision	Large, short-duration	Separate or stuck
Explosion	Internal forces push apart	Separate, moving in opposite directions

4.2

Change in Momentum and Impulse

The net external force on a system equals the rate of change of its momentum: F_net = dp/dt. Impulse J is the integral of net force over a time interval, J = integral from t1 to t2 of F_net(t) dt, and equals the change in momentum delta p. Impulse is a vector in the direction of the net force. Graphically, impulse is the area under a force-time curve, and net force is the slope of a momentum-time graph.

F_net = dp/dt: Newton's second law in momentum form; for constant mass this reduces to F_net = ma.
J = integral of F_net dt = delta p: The impulse-momentum theorem: impulse equals change in momentum, linking force, time, and velocity change.
Area under F vs. t graph: The area under the curve of a force-time graph gives the impulse delivered during that interval.
Slope of p vs. t graph: The slope of a momentum-time graph at any point equals the net external force at that instant.
Variable mass case: When mass changes with time, F_net = dp/dt = (dm/dt)v, which applies to rocket propulsion problems.

A force varies with time as shown on a graph. How would you find the impulse delivered between t = 0 and t = 4 s without a constant force?

Graph type	Slope represents	Area represents
Force vs. time	Rate of change of force	Impulse (delta p)
Momentum vs. time	Net external force	Not directly used

4.3

Conservation of Linear Momentum

When the net external force on a system is zero, total momentum is conserved: the sum of initial momenta equals the sum of final momenta. Internal forces between objects cancel by Newton's third law, so they do not change total system momentum. The center-of-mass velocity is v_cm = (sum of m_i * v_i) / (sum of m_i), and it remains constant in the absence of a net external force. Conservation applies component-wise in 2D problems.

Isolated system: A system with no net external force, so total momentum is constant throughout any internal interaction.
v_cm = sum(m_i * v_i) / sum(m_i): Center-of-mass velocity equals total momentum divided by total mass; constant when no net external force acts.
Newton's third law cancellation: Action-reaction force pairs are internal to the system and cancel, leaving only external forces to change total momentum.
Component-wise conservation: In 2D collisions, momentum is conserved separately in the x- and y-directions, giving two independent equations.
System selection: Choosing which objects to include in the system determines which forces are internal and which are external.

A 3 kg cart moving at 4 m/s east collides with a stationary 1 kg cart. If they stick together, what is the final velocity of the combined system?

Condition	Is momentum conserved?	Reason
No net external force	Yes	Internal forces cancel by Newton's third law
Net external force present	No	External impulse changes total momentum
Explosion (internal forces only)	Yes	No net external force on the system

4.4

Elastic and Inelastic Collisions

Momentum is conserved in all collisions when the system is isolated. The collision type is determined by what happens to kinetic energy. In an elastic collision, total kinetic energy is the same before and after. In an inelastic collision, total kinetic energy decreases because nonconservative forces convert some kinetic energy into heat, sound, or deformation. In a perfectly inelastic collision, the objects stick together and share a common final velocity.

Elastic collision: Both momentum and total kinetic energy are conserved; individual object kinetic energies may change.
Inelastic collision: Momentum is conserved but total kinetic energy decreases; energy is lost to nonconservative processes.
Perfectly inelastic collision: Objects stick together after the collision and move with the same final velocity; maximum kinetic energy is lost.
Kinetic energy check: Compare (1/2)mv^2 totals before and after; if equal, elastic; if less after, inelastic.
Two equations for elastic 1D: Use conservation of momentum and conservation of kinetic energy together to solve for two unknown final velocities.

Two objects collide and stick together. Is kinetic energy conserved? How do you find the final velocity?

Collision type	Momentum conserved?	KE conserved?	Objects after
Elastic	Yes	Yes	Separate
Inelastic	Yes	No (decreases)	Separate
Perfectly inelastic	Yes	No (maximum loss)	Stuck together

Key terms

Term	Definition
collision	A model for an interaction between objects in which the internal forces are much larger than any net external force, so only initial and final states need to be analyzed.
explosion	A model for an interaction in which forces internal to a system push objects within that system apart; total system momentum is conserved.
impulse-momentum theorem	States that the impulse delivered to an object equals its change in momentum: J = integral of F_net dt = delta p.
perfectly inelastic collision	A collision in which the objects stick together and move with the same final velocity; kinetic energy loss is at its maximum for that momentum exchange.
area under the curve	On a force-time graph, the area under the curve equals the impulse delivered to the object during that time interval.
object model	A simplifying model that treats each object as a point mass, ignoring size and internal structure, which is valid for analyzing collisions.

How to review unit 4

Topics students miss most

Miss rates come from Fiveable multiple-choice practice.

4.2

Change in Momentum and Impulse

35%547 tries

Common unit 4 mistakes

Ignoring the vector nature of momentum

Momentum has direction. In 1D problems, assign positive and negative signs based on direction before calculating. In 2D, split into x- and y-components and conserve each separately.

Confusing impulse with force

Impulse is the integral of force over time, not force alone. A large force over a short time and a small force over a long time can deliver the same impulse. Always multiply or integrate with the time interval.

Assuming kinetic energy is conserved in all collisions

Kinetic energy is only conserved in elastic collisions. In any inelastic collision, including perfectly inelastic ones, total kinetic energy decreases. Momentum is always conserved in an isolated system regardless of collision type.

Applying conservation of momentum when a net external force acts

Conservation of momentum requires that the net external impulse on the system is zero. If gravity, friction, or another external force acts during the interaction and is not negligible, total momentum changes.

Using the wrong final velocity in a perfectly inelastic collision

When objects stick together, they share one final velocity. Set up m1v1 + m2v2 = (m1 + m2)*v_f and solve for v_f. Do not use separate final velocities for each object.

How this unit shows up on the AP exam

Calculus-based impulse calculations

AP Physics C: Mechanics problems frequently give a force as a function of time and ask you to integrate to find impulse, or present a force-time graph and ask for the area. Be ready to set up and evaluate definite integrals and to read graphical data accurately.

Multi-step collision problems combining momentum and energy

Free-response problems often require you to apply conservation of momentum to find a post-collision velocity, then use that result in a separate energy or kinematics calculation. Recognizing which conservation law applies at each stage is the central skill.

Justifying whether momentum is conserved

Exam questions ask you to explain in words why momentum is or is not conserved in a given scenario. A complete answer names the system, identifies whether a net external force acts, and references Newton's third law for internal force cancellation.

More ways to review

Topic study guides

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Practice questions

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Frequently Asked Questions

What's on the AP Physics Mech Unit 4 progress check (MCQ and FRQ)?

The AP Physics C: Mechanics Unit 4 progress check in AP Classroom includes both MCQ and FRQ parts drawn from all four unit topics: Linear Momentum, Change in Momentum and Impulse, Conservation of Linear Momentum, and Elastic and Inelastic Collisions. The MCQ section tests conceptual understanding and calculation, while the FRQ part asks you to set up and solve multi-step problems involving impulse-momentum and collision scenarios. For the progress check, focus on applying the impulse-momentum theorem correctly and distinguishing elastic from inelastic collisions. You can find matched practice problems at AP Physics C: Mechanics Unit 4.

How do I practice AP Physics Mech Unit 4 FRQs?

Unit 4 FRQs in AP Physics C: Mechanics most often come from Conservation of Linear Momentum and Elastic and Inelastic Collisions, so those two topics should anchor your free-response practice. A typical FRQ will ask you to define a system, justify why momentum is conserved, set up conservation equations, and solve for an unknown velocity or energy loss. To practice effectively:
- Write out your system definition and conservation statement before calculating
- Show all vector directions explicitly, since momentum is a vector quantity
- Practice both perfectly inelastic and elastic collision setups, as each has a different equation structure
- Check your work by verifying units and the reasonableness of your answer Find FRQ-style practice problems at AP Physics C: Mechanics Unit 4.

Where can I find AP Physics Mech Unit 4 practice questions?

The best place to find AP Physics C: Mechanics Unit 4 practice questions, including multiple-choice and practice test problems, is AP Physics C: Mechanics Unit 4. That page has resources covering all four topics: Linear Momentum, Change in Momentum and Impulse, Conservation of Linear Momentum, and Elastic and Inelastic Collisions. For MCQ practice, look for questions that ask you to calculate impulse, compare momentum before and after a collision, or identify whether kinetic energy is conserved. These are the most common question formats for this unit on the actual exam.

How should I study AP Physics Mech Unit 4?

Start with the impulse-momentum theorem in Topic 4.2 before moving to conservation laws, since understanding how force and time change momentum makes Topic 4.3 much more intuitive. Unit 4 rewards students who practice setting up problems systematically rather than jumping straight to equations. A solid study plan for this unit:
1. Build the foundation first. Make sure you can define momentum as a vector and apply p = mv in multiple dimensions before tackling collisions.
2. Master the impulse-momentum theorem. Practice interpreting force-time graphs and calculating impulse from area under the curve.
3. Drill conservation of momentum. Write out system definitions and justify conservation conditions every time, not just when the problem asks you to.
4. Separate collision types clearly. Know that elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve only momentum.
5. Do timed FRQ practice. Since this unit is 10-20% of the exam, free-response problems here are high value. All four topics are organized at AP Physics C: Mechanics Unit 4.

Ready to review Unit 4?Start with the notes, check the topic cards, and use the practice or resource links when they are available for this course.

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