AP Physics 1 Unit 4: Linear Momentum Notes

Introduction

Momentum tracks mass in motion, while external impulse determines how the total momentum of a chosen system changes during an interval.

Momentum is a vector state quantity: its components must be added with signs or directions intact. Impulse is the mechanism for changing momentum. During a short collision, the interaction forces inside a well-chosen system may be large while the net external impulse remains small, allowing a conservation model.

Momentum conservation does not automatically conserve kinetic energy. Classify a collision by comparing the total kinetic energy before and after, after first confirming whether external impulse is negligible.

Mass and velocity

linear momentum

Net force over time

impulse and momentum change

Negligible external impulse

system momentum conservation

Kinetic-energy comparison

collision classification

Current exam guidance: Aligned to the current 2026–27 AP Physics 1 framework, with algebra-based modeling, experimental reasoning, and explicit assumptions.

4.1

Linear Momentum

How do mass and velocity jointly determine linear momentum?

Short answer

Linear momentum is $\vec p=m\vec v$ , so it scales with mass, points with velocity, and adds by vector components across a system.

Know firstMass and inertia · Velocity vectors · System choice

Keep direction inside the momentum ledger

Choose a system and coordinate axis before assigning momentum. Positive mass means an object’s momentum points in the same direction as its velocity. Reversing velocity reverses momentum, unlike kinetic energy. A system’s total momentum is the vector sum of its parts, so two large opposing momenta can cancel even though both objects are moving.

Momentum depends on the reference frame because velocity does. Inertia is the resistance to changing velocity and depends on mass; momentum is not a substitute word for inertia or force. In a collision model, objects interact strongly over a short interval. In an explosion model, internal interactions separate parts, but they cannot create net system momentum without external impulse.

Physics model

Momentum carries both magnitude and direction

Reverse velocity and watch the momentum vector reverse while kinetic energy remains nonnegative.

Velocity5 m/s

Velocity: 5 m/s
Momentum: 10 kg·m/s
Kinetic energy: 25 J

massvelocity vectormomentum vector

\vec p=m\vec v

Read this figure without the graphic

Reverse velocity and watch the momentum vector reverse while kinetic energy remains nonnegative. The table below states the model assumptions and relationships without relying on color or motion.

Quantity	Meaning
Momentum	Signed vector $m\vec v$
Kinetic energy	Scalar $\tfrac12mv^2$
Zero momentum	Requires zero velocity for nonzero mass

Build a signed system total

System: All objects included in the momentum sum.
Frame: One inertial frame with rightward velocity positive.
Assumptions: Each object has constant mass during the modeled interval.
Givens: Each mass and signed velocity.

Assign a signed velocity or vector components to every object.
Multiply each velocity by its object’s mass.
Add matching components to obtain the system total.

Result

\vec p_{\mathrm{system}}=\sum_i m_i\vec v_i

Units:

\mathrm{kg\,m/s}

Boundary cases

Opposing nonzero momenta may sum to zero.
A moving frame changes every velocity and can change total momentum.

System momentum is the vector sum of mass times velocity for every included object.

Opposing momenta can cancel

Object	Mass	Velocity	Momentum	Kinetic energy
A	$2\ \mathrm{kg}$	$+3\ \mathrm{m/s}$	$+6\ \mathrm{kg\,m/s}$	$9\ \mathrm J$
B	$3\ \mathrm{kg}$	$-2\ \mathrm{m/s}$	$-6\ \mathrm{kg\,m/s}$	$6\ \mathrm J$
system	$5\ \mathrm{kg}$	not one object velocity	$0$	$15\ \mathrm J$

Assemble a momentum state

Name the system and frame.
Choose coordinate signs.
Calculate each object’s vector momentum.
Add components, then interpret the system result without erasing individual motion.

Measure momentum with photogates

Do measured masses and velocities reproduce a signed momentum balance?

Variables: Measured: mass and velocity; calculated response: momentum; control: one track coordinate system.
Apparatus: Two low-speed carts, level track, balance, photogates, and catch stops.
Procedure boundary: Keep cart speeds low and confirm photogate flags cannot detach.
Uncertainty: Combine balance resolution and velocity timing uncertainty; check track level for systematic drift.

Measure momentum with photogates lab dataset
Object	Mass (kg)	Velocity (m/s)	Momentum (kg m/s)
A	2	3	6
B	3	-2	-6

Provided accessible table

Measure momentum with photogates accessible table
Object	Mass kg	Velocity m/s	Momentum kg m/s
A	2	3	6
B	3	-2	-6

Keep these three ideas

Momentum is mass times vector velocity.
System totals use component addition.
Momentum and inertia describe different physical ideas.

Linear Momentum

Introduction

Linear Momentum

Keep direction inside the momentum ledger

Momentum carries both magnitude and direction

Build a signed system total

Boundary cases

Opposing momenta can cancel

Assemble a momentum state

Measure momentum with photogates

Keep these three ideas

Keep reading Unit 4: Linear Momentum

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