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AP Physics 1 Unit 4 Review: Linear Momentum

Review AP Physics 1 Unit 4 to build fluency with linear momentum, impulse, and the conservation laws that govern collisions and explosions. This unit carries 10-15% of the exam and connects directly to force, energy, and rotational momentum in later units.

Use the topic guides, practice questions, and FRQ practice available here to work through every major concept before exam day.

What is AP Physics 1 unit 4?

Linear momentum is one of the most powerful tools in mechanics because it lets you analyze interactions between objects without tracking every detail of the forces involved. Unit 4 builds from the definition of momentum through impulse, conservation laws, and collision types.

Linear momentum (p = mv) is a vector. When no net external force acts on a system, total momentum is conserved. Impulse equals the change in momentum. Collisions are elastic if kinetic energy is conserved and inelastic if it is not.

Momentum is a vector

Because p = mv and velocity is a vector, momentum has both magnitude and direction. In one-dimensional problems, sign conventions (positive and negative directions) are essential for getting correct answers in collisions and explosions.

Impulse connects force and momentum

The impulse-momentum theorem states J = F_avg * delta_t = delta_p. This means a large force over a short time or a small force over a long time can produce the same momentum change. The area under a force-time graph equals the impulse delivered.

System selection determines conservation

Momentum is conserved only when the net external force on the chosen system is zero. Choosing which objects to include in your system determines whether momentum is constant or changes due to an external impulse from the surroundings.

Why momentum conservation is so useful

During a collision, internal forces between objects are enormous and short-lived, making Newton's second law hard to apply directly. Momentum conservation sidesteps this by comparing only the total momentum before and after the interaction. As long as the system is isolated, the messy details of the collision forces do not matter.

AP Physics 1 unit 4 topics

4.1

Linear Momentum

Defines momentum as p = mv, establishes its vector nature, and introduces the collision and explosion models as frameworks for analyzing interactions using only initial and final states.

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4.2

Change in Momentum and Impulse

Connects force and time to momentum change through the impulse-momentum theorem J = F_avg * delta_t = delta_p, and links force-time graphs and momentum-time graphs to these quantities.

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4.3

Conservation of Linear Momentum

Establishes that total momentum is constant in an isolated system, introduces center-of-mass velocity, and explains how system selection determines whether momentum is conserved or changes.

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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 together). Momentum is conserved in all types.

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practice snapshot

Hardest AP Physics 1 unit 4 topics

This snapshot uses Fiveable practice activity to show where students tend to miss questions and which review moves are worth prioritizing first.

59%average MCQ accuracy

Across 3.6k multiple-choice practice attempts for this unit.

3.6kMCQ attempts

Practice activity included in this snapshot.

64%average FRQ score

Across 12 scored free-response attempts for this unit.

Hardest topics in unit 4

MCQ miss rate
4.4

Review Elastic and Inelastic Collisions with attention to how the concept appears in AP-style source and evidence questions.

46%746 tries
4.2

Review Change in Momentum and Impulse with attention to how the concept appears in AP-style source and evidence questions.

39%1,204 tries

Unit 4 review notes

4.1

Linear Momentum

Linear momentum is defined as p = mv, where p is a vector pointing in the same direction as velocity. For a system of objects, the total momentum is the vector sum of each object's individual momentum. Momentum is the primary tool for analyzing collisions and explosions because it compares only initial and final states.

  • p = mv: Linear momentum equals mass times velocity. Doubling speed doubles momentum; doubling mass doubles momentum.
  • Vector direction: Momentum points in the same direction as velocity. In 1D problems, assign positive and negative signs carefully before calculating.
  • Collision model: A collision is modeled as an interaction where internal forces between objects far exceed any net external force, so the object model applies and only initial and final states are analyzed.
  • Explosion model: An explosion is an interaction where internal forces push objects within the system apart. Total momentum before and after is still conserved if the system is isolated.
A 2 kg cart moves at 3 m/s east. What is its momentum? If it reverses direction at the same speed, what is the new momentum?
Interaction typeInternal forcesObjects beforeObjects after
CollisionPush objects together or apart brieflySeparate, movingMay stick or bounce
ExplosionPush objects apartTogether or at restSeparate, moving apart
4.2

Change in Momentum and Impulse

Impulse J equals the average net force times the time interval over which it acts: J = F_avg * delta_t. By the impulse-momentum theorem, this equals the change in momentum: J = delta_p. The net force also equals the rate of change of momentum: F_net = delta_p / delta_t. On a force-time graph, the area under the curve is the impulse; on a momentum-time graph, the slope is the net force.

  • Impulse J = F_avg * delta_t: Impulse is a vector with the same direction as the net force. Units are N*s, which are equivalent to kg*m/s.
  • Impulse-momentum theorem: J = delta_p. The impulse delivered to an object equals its change in momentum, regardless of how the force varies during the interval.
  • Force-time graph area: The area under a force vs. time curve equals the impulse. For a constant force, the area is a rectangle; for a variable force, estimate or calculate the area geometrically.
  • Momentum-time graph slope: The slope of a momentum vs. time graph at any point equals the net force acting on the object at that moment.
  • Rebound sign reversal: When an object bounces back, its momentum changes direction. Calculate delta_p = p_final - p_initial carefully using signed values, not just magnitudes.
A 0.5 kg ball hits a wall at 4 m/s and rebounds at 4 m/s. What is the magnitude of the impulse delivered to the ball? If the contact time is 0.02 s, what is the average force?
Graph typeSlope representsArea represents
Force vs. timeRate of change of force (not directly useful)Impulse delivered
Momentum vs. timeNet force on the objectNot directly used
4.3

Conservation of Linear Momentum

In an isolated system (net external force = 0), the total momentum before an interaction equals the total momentum after. Any momentum change in one object within the system is balanced by an equal and opposite change in another object, consistent with Newton's third law. The center-of-mass velocity of the system remains constant when no net external force acts.

  • Isolated system condition: Momentum is conserved only when the net external force on the system is zero. If a nonzero external force acts, momentum is transferred between the system and its surroundings.
  • Total momentum conservation: Sum of p_i before = sum of p_i after. In 1D, use signed values. In 2D, apply conservation separately to x and y components.
  • Center-of-mass velocity: v_cm = (sum of m_i * v_i) / (sum of m_i). This velocity is constant when no net external force acts on the system.
  • Newton's third law link: The impulse one object exerts on another is equal in magnitude and opposite in direction, so internal forces cannot change the total momentum of the system.
  • System selection: Choosing which objects to include in the system determines whether momentum is conserved. A force that is external to one system choice may be internal to a larger system choice.
A 3 kg cart moving at 2 m/s east collides with a stationary 1 kg cart. After the collision, the 3 kg cart moves at 0.5 m/s east. What is the velocity of the 1 kg cart after the collision?
System conditionNet external forceTotal momentum
Isolated systemZeroConstant (conserved)
Non-isolated systemNonzeroChanges by the external impulse
4.4

Elastic and Inelastic Collisions

Collisions are classified by what happens to the total kinetic energy of the system. In an elastic collision, total kinetic energy is conserved. In an inelastic collision, total kinetic energy decreases because some energy is converted to thermal energy, sound, or deformation. In a perfectly inelastic collision, the objects stick together and move at a single shared velocity, which represents the maximum possible kinetic energy loss. Momentum is conserved in all collision types.

  • Elastic collision: Total kinetic energy of the system is the same before and after. Individual objects may exchange kinetic energy, but the total does not change.
  • Inelastic collision: Total kinetic energy decreases. The lost kinetic energy is converted to other forms by nonconservative forces during the interaction.
  • Perfectly inelastic collision: Objects stick together and move with a common velocity after the collision. Use p_total_before = (m1 + m2) * v_common to find the shared velocity.
  • Kinetic energy loss calculation: delta_KE = KE_final - KE_initial. This value is zero for elastic, negative for inelastic. It is never positive in a standard collision.
  • Momentum conserved in all cases: Regardless of collision type, if the system is isolated, total momentum is conserved. Kinetic energy conservation is an additional condition only for elastic collisions.
A 4 kg block moving at 6 m/s collides and sticks to a stationary 2 kg block. Find the common velocity after the collision and the kinetic energy lost.
Collision typeMomentum conserved?Kinetic energy conserved?Objects after
ElasticYesYesSeparate, may exchange speeds
InelasticYesNo (decreases)Separate, some KE lost
Perfectly inelasticYesNo (maximum loss)Stick together, one velocity

Practice AP Physics 1 unit 4 questions

Try stimulus-based AP practice questions and written prompts after you review the notes.

Example stimulus-based MCQs

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setup_diagram

Stimulus-based practice question

Two carts containing strong magnets, with masses m1m_1 and m2m_2, slide toward each other on a horizontal frictionless track, as shown in the figure. The carts repel and reverse direction without touching.

Question

Which claim correctly describes the system’s total momentum during the interaction?

System Cart 1 only. Momentum stays constant because magnetic force is noncontact.

System Cart 1 and Cart 2. Momentum stays constant because magnetic forces are internal.

System Cart 1 and Cart 2. Momentum changes because both carts accelerate under magnetic force.

System Cart 1, Cart 2, and the track. Momentum changes because the track’s normal force is external.

visual_answers

Stimulus-based practice question

Cart 1 of mass mm travels at speed v0v_0 and collides with stationary Cart 2 of mass mm. The graph shows the velocities of both carts before and after the collision for two different trials. Trial 1 shows the carts exchanging velocities. Trial 2 shows the carts moving together at the same final velocity.

Question

Which of the following energy bar charts could represent the total kinetic energy of the two-cart system after the collision in Trial 1 (K1K_1) and Trial 2 (K2K_2), compared to the initial total kinetic energy (K0K_0)?

Answer choice A
Answer choice B
Answer choice C
Answer choice D

Example FRQs

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FRQ

Momentum conservation in inelastic collisions

2. Two low-friction carts move along a straight horizontal track and collide.

Figure 1. Two carts on a straight horizontal track, shown at two instants: immediately before collision and immediately after collision.

Figure 1

Figure 2. Momenta of carts just before the collision (bar chart template with fixed scale).

Figure 2

Figure 3. Momenta of carts just after the collision (same scale as Figure 2).

Figure 3
A.

Draw shaded bars to represent the momenta pAp_A and pBp_B just before the collision (Figure 2) and just after the collision (Figure 3). Momentum is a vector quantity. Consider the system consisting of cart A and cart B. Take rightward momentum to be positive. Using Figure 1 and the momentum bar chart templates in Figures 2 and 3 for the carts just before and just after the collision.

• Shaded bars should start at the line that represents zero momentum.
• Represent any momentum that is equal to zero with a distinct line on the zero-momentum line.
• The relative heights of the shaded bars should reflect the magnitudes and signs of the momenta, using the same scale in both figures.

B.

Starting with a fundamental physics principle, derive an expression for the final speed vB,fv_{B,f} of cart B after the collision. Express your answer in terms of mAm_A, mBm_B, vA,iv_{A,i}, and vA,fv_{A,f}. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Assume the net external impulse on the two-cart system during the collision is negligible.

Figure 4. Axes for force on cart A versus time during the 0.25 s collision.

Figure 4
C.

Figure 4 shows axes for a graph of the force FAF_A exerted on cart A by cart B as a function of time during the collision, from t=0t=0 to t=0.25 st=0.25\ \text{s}. The impulse on cart A during the collision is JA=00.25sFAdtJ_A=\int_0^{0.25\,s}F_A\,dt.

i.

Sketch and label a possible graph of FAF_A versus tt on Figure 4 that is consistent with the change in momentum of cart A during the collision.

ii.

Sketch and label on Figure 4 a second, different possible graph of FAF_A versus tt that is also consistent with the change in momentum of cart A during the collision.

D.

Indicate whether the collision between the carts is elastic, perfectly inelastic, or inelastic (but not perfectly inelastic).

elastic
perfectly inelastic
inelastic (but not perfectly inelastic)
Justify how your response is consistent with the momentum representations in part A and the value you derived for vB,fv_{B,f} in part B, including a comparison of the total kinetic energy of the two-cart system before and after the collision.

FRQ

Linear momentum and mass determination during collisions

3. Students are investigating linear momentum during collisions using the following setup.

A.

Describe an experimental procedure to collect data that would allow the students to determine mAm_A. Include any steps necessary to reduce experimental uncertainty.

B.

Describe how the data collected in part A could be graphed and how that graph would be analyzed to determine mAm_A.

Figure 1. Single–motion-sensor momentum-collision setup (cart B initially at rest; cart A has unknown mass).

Figure 1

Figure 2. Two–motion-sensor setup to measure both carts’ velocities before and after collision; bumpers fitted with plastic caps.

Figure 2

vAi (m/s)v_{Ai}\ (\text{m/s})

vAf (m/s)v_{Af}\ (\text{m/s})

0.60

0.11

0.80

0.15

1.00

0.18

1.20

0.22

1.40

0.27

vAi (m/s)v_{Ai}\ (\text{m/s})

vAf (m/s)v_{Af}\ (\text{m/s})

(blank for student calculations)

C.

The students modify the setup by placing smooth plastic caps over the bumpers so that the collision is closer to elastic, as shown in Figure 2. Cart B is again initially at rest. The students perform several trials, each time launching cart A so that it has a different initial speed vAiv_{Ai}. For each trial, the students measure vAiv_{Ai} and the final speed of cart A after the collision, vAfv_{Af}. Table 1 shows the measured values.

The students correctly determine that the relationship between vAfv_{Af} and vAiv_{Ai} is vAf=(mAemBmA+mB)vAiv_{Af} = \left(\dfrac{m_A - e m_B}{m_A + m_B}\right) v_{Ai}, where mB=0.50 kgm_B = 0.50\ \text{kg} and ee is the coefficient of restitution for the collision.

The students create a graph with vAiv_{Ai} plotted on the horizontal axis.

i.

Indicate what measured or calculated quantity could be plotted on the vertical axis to yield a linear graph whose slope can be used to calculate an experimental value for the mass mAm_A of cart A.

Vertical axis: Horizontal axis: vAiv_{Ai}

ii.

On the blank grid provided, create a graph of the quantities indicated in part C(i) that can be used to determine mAm_A.

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

Clearly label the vertical axis, including units as appropriate.

Plot the points you recorded in Table 2.

iii.

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

D.

Using the best-fit line that you drew in part C(iii), calculate an experimental value for the mass mAm_A of cart A. Using the graph from part C, the students determine that the slope of the best-fit line is s=0.19s = 0.19 (unitless).

In a separate calibration trial using the same bumpers and plastic caps, the students measure the coefficient of restitution to be e=0.80e = 0.80.

Assume external horizontal forces on the two-cart system are negligible during the collision.

FRQ

Momentum conservation in collision systems

4. In Scenario 1, a low-friction cart A of mass mA=0.60 kgm_A = 0.60\ \text{kg} moves to the right on a horizontal track with speed v0=3.0 m/sv_0 = 3.0\ \text{m/s}. Cart A collides head-on with cart B, which is initially at rest and has mass mB1=0.40 kgm_{B1} = 0.40\ \text{kg}, as shown in Figure 1. The carts stick together during the collision. All external horizontal forces on the two-cart system are negligible during the collision.

In Scenario 2, cart A is again moving to the right with speed v0=3.0 m/sv_0 = 3.0\ \text{m/s} on the same horizontal track. Cart A collides head-on with a different cart B that is initially at rest but has mass mB2=1.20 kgm_{B2} = 1.20\ \text{kg}, as shown in Figure 1. The carts again stick together during the collision. All external horizontal forces on the two-cart system are negligible during the collision.

Figure 1. Two head-on, perfectly inelastic collisions on a horizontal low-friction track: Scenario 1 uses cart B of mass 0.40 kg; Scenario 2 uses cart B of mass 1.20 kg. Cart A (0.60 kg) approaches at 3.0 m/s to the right, the carts stick, and the combined carts move right with final speed v1 (Scenario 1) or v2 (Scenario 2).

Figure 1
A.

Refer to Figure 1. Indicate whether v1v_1 is greater than, less than, or equal to v2v_2 by writing one of the following in your answer booklet.

v1>v2v_1 > v_2
v1<v2v_1 < v_2
v1=v2v_1 = v_2

Justify your answer in terms of the selection of a system and whether the momentum of that system changes during the collision. Use qualitative reasoning beyond referencing equations.

B.

Starting with the definition of linear momentum and the conservation of linear momentum for an appropriately chosen system, derive an expression for the common final speed vfv_f after the collision. Express your answer in terms of mAm_A, mBm_B, and v0v_0. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Consider the general case in which cart A (mass mA=0.60 kgm_A = 0.60\ \text{kg}) moves with initial speed v0=3.0 m/sv_0 = 3.0\ \text{m/s} and collides with cart B (initially at rest) of mass mBm_B. The carts stick together and move with common final speed vfv_f. External horizontal forces on the two-cart system are negligible during the collision.

C.

Indicate whether the expression for vfv_f you derived in part B is or is not consistent with the claim made in part A. Briefly justify your answer by referencing your derivation in part B and describing how vfv_f depends on mBm_B. Also describe whether the interaction between the carts is elastic or inelastic and how your conclusion is supported by the collision description.

Key terms

TermDefinition
explosionA model for an interaction in which internal forces within a system move objects within that system apart. Total momentum of the system is conserved if no net external force acts.
force-time graphA graphical representation of force as a function of time, where the area under the curve represents the impulse delivered to an object.
object modelA simplification in which an object's size, shape, and internal configuration are ignored, and the object is treated as a single point with properties such as mass. Used when analyzing collisions.

Common unit 4 mistakes

Ignoring the sign of momentum in 1D problems

Momentum is a vector. If an object moves left and you assign rightward as positive, its momentum is negative. Forgetting signs when objects move in opposite directions leads to incorrect conservation equations.

Assuming kinetic energy is always conserved in collisions

Kinetic energy is conserved only in elastic collisions. Most real collisions are inelastic. Do not use energy conservation to find post-collision velocities unless the problem explicitly states the collision is elastic.

Applying momentum conservation to a non-isolated system

Momentum is conserved only when the net external force on the system is zero. If friction, gravity, or a normal force has a net effect on the system during the interaction, total momentum changes.

Confusing impulse magnitude with force magnitude

A large impulse does not require a large force. A small force acting over a long time can produce the same impulse as a large force over a short time. Always account for both force and time interval.

Using magnitudes instead of signed values when calculating delta_p

When an object rebounds, its momentum changes direction. delta_p = p_final - p_initial must use signed values. For a ball bouncing back at the same speed, the magnitude of delta_p is twice the magnitude of the initial momentum, not zero.

How this unit shows up on the AP exam

Quantitative reasoning with conservation equations

Free-response questions in this unit typically ask you to set up and solve a conservation of momentum equation for a collision or explosion, then calculate a post-interaction velocity. You may also be asked to calculate kinetic energy before and after to determine whether a collision is elastic or inelastic and to find the energy lost.

Graph interpretation for impulse and force

Multiple-choice and free-response questions frequently present force-time or momentum-time graphs and ask you to extract impulse from area, net force from slope, or to compare impulses delivered to two objects. Be ready to connect a graph feature to a physical quantity using the impulse-momentum theorem.

Justifying system selection and conservation conditions

Questions often ask you to explain why momentum is or is not conserved in a given scenario. You need to identify the system, state whether the net external force is zero, and explain how that determines whether total momentum changes. This reasoning task appears in both short justification items and longer free-response parts.

Final unit 4 review checklist

  • Calculate momentum correctly as a vectorApply p = mv with correct sign conventions in 1D. For 2D problems, resolve velocity into components before calculating momentum in each direction.
  • Apply the impulse-momentum theoremUse J = F_avg * delta_t = delta_p to connect force, time, and momentum change. Extract impulse from the area under a force-time graph and net force from the slope of a momentum-time graph.
  • Set up conservation of momentum equationsWrite sum of p_before = sum of p_after for the system. Confirm the system is isolated (net external force = 0) before applying conservation. Use signed values in 1D.
  • Identify the collision type and apply the right toolsDetermine whether a collision is elastic, inelastic, or perfectly inelastic. For perfectly inelastic collisions, use (m1 + m2) * v_common. For elastic collisions, both momentum and kinetic energy are conserved.
  • Calculate kinetic energy loss in inelastic collisionsFind KE_initial and KE_final using KE = (1/2)mv^2 for each object, then compute delta_KE = KE_final - KE_initial. This value should be negative or zero.
  • Use center-of-mass velocity for system analysisApply v_cm = (sum of m_i * v_i) / (sum of m_i) to describe the system as a whole. Recognize that v_cm is constant when no net external force acts on the system.
  • Connect momentum to Newton's third lawExplain why internal forces cannot change total system momentum: the impulse one object exerts on another is equal and opposite, so internal impulses cancel in the total.

How to study unit 4

Start with Topic 4.1: momentum as a vectorRead the Topic 4.1 guide and practice calculating p = mv with correct signs. Work through examples involving objects moving in opposite directions and confirm you can describe the total momentum of a two-object system.
Move to Topic 4.2: impulse and force-time graphsStudy the impulse-momentum theorem using the Topic 4.2 guide. Practice reading force-time graphs to find impulse from area and momentum-time graphs to find net force from slope. Try rebound problems where momentum changes sign.
Work through Topic 4.3: conservation of momentumUse the Topic 4.3 guide to set up conservation equations for collisions and explosions. Practice choosing a system, checking whether it is isolated, and applying sum of p_before = sum of p_after in 1D scenarios.
Finish with Topic 4.4: collision types and energyReview the Topic 4.4 guide to distinguish elastic, inelastic, and perfectly inelastic collisions. Practice calculating kinetic energy before and after to classify a collision and find energy lost. Use the AP score calculator to estimate your overall exam standing.

More ways to review

Topic study guides

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Frequently Asked Questions

What topics are covered in AP Physics 1 Unit 4?

AP Physics 1 Unit 4 covers four topics: **4.1 Linear Momentum**, **4.2 Change in Momentum and Impulse**, **4.3 Conservation of Linear Momentum**, and **4.4 Elastic and Inelastic Collisions**. Together, these topics build from defining momentum as mass times velocity all the way to predicting what happens when objects collide or explode apart. See practice and study materials at AP Physics 1 Unit 4.

How much of the AP Physics 1 exam is Unit 4?

Unit 4: Linear Momentum makes up 10-15% of the AP Physics 1 exam, making it one of the more heavily tested units. That weight covers momentum, impulse, conservation of linear momentum, and elastic and inelastic collisions. Expect at least a few multiple-choice questions and a possible FRQ drawing from these concepts.

What's on the AP Physics 1 Unit 4 progress check (MCQ and FRQ)?

The AP Physics 1 Unit 4 progress check includes both MCQ and FRQ parts drawn from all four unit topics: linear momentum, impulse and change in momentum, conservation of linear momentum, and elastic and inelastic collisions. The MCQ section tests conceptual understanding and calculations, while the FRQ part asks you to explain and justify momentum-based reasoning in multi-step scenarios. For matched practice problems that mirror the progress check format, visit AP Physics 1 Unit 4.

How do I practice AP Physics 1 Unit 4 FRQs?

The best way to practice AP Physics 1 Unit 4 FRQs is to focus on the topics that generate the most free-response questions: conservation of linear momentum and elastic and inelastic collisions. These questions typically ask you to set up momentum equations, justify whether momentum is conserved, and compare kinetic energy before and after a collision. Practice by writing out full solutions with clear diagrams and written justifications, not just numbers. Find Unit 4 FRQ practice at AP Physics 1 Unit 4.

Where can I find AP Physics 1 Unit 4 practice questions?

You can find AP Physics 1 Unit 4 multiple-choice and practice test questions at AP Physics 1 Unit 4. That page has MCQ practice covering momentum calculations, impulse problems, and collision scenarios, along with FRQ-style questions to help you prep for the full exam. Working through a mix of question types is the most effective way to get ready for the Unit 4 content on test day.

How should I study AP Physics 1 Unit 4?

Start by making sure you can define momentum and set up the impulse-momentum theorem before moving on to conservation problems. A solid study plan for Unit 4 looks like this: 1. **Learn the definitions first.** Know that momentum equals mass times velocity, and that impulse equals force times time. 2. **Practice impulse problems.** These show up constantly and require connecting force, time, and change in momentum. 3. **Master conservation of linear momentum.** Identify isolated systems and write out momentum equations for both objects before and after an interaction. 4. **Distinguish collision types.** Know what makes a collision elastic versus inelastic, and what is and is not conserved in each case. 5. **Do timed FRQ practice.** Write out full justifications, not just equations. Visit AP Physics 1 Unit 4 for practice materials organized by topic.

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.