Momentum carries the direction of motion
You will be able to: Calculate signed momentum and resolve a momentum vector into components.
How do mass and velocity combine into momentum?
A 2 kg cart moving right at 3 m/s has momentum +6 kg·m/s if right is positive. Turn it around at the same speed and its momentum is −6 kg·m/s. Direction is part of the quantity.
A useful starting point: Describe a vector with components →
Words and symbols before equations
- Linear momentum p
- Mass times velocity, p = mv; a vector measured in kg·m/s.
- Velocity v
- Speed together with direction; use m/s.
- Component
- The signed amount of a vector along a chosen axis.
- Magnitude |p|
- Length of the momentum vector, equal to mass times speed for positive mass.
What this picture assumes
One point object in a fixed inertial frame. Momentum components use the same kg·m/s scale. Axes are momentum axes, not spatial positions.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- p = (6, 0) kg·m/s; magnitude 6 kg·m/s. Dashed lines project this one momentum vector; they are not additional momenta.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Choose axes and a reference frame before using signs. In one dimension, pₓ = mvₓ; negative momentum means motion along the negative axis, not a negative amount of mass.
In a plane, pₓ = mvₓ and pᵧ = mvᵧ. Add components to combine momenta, then find the magnitude using √(pₓ² + pᵧ²). Adding magnitudes first loses the direction information.
Momentum is useful for short interactions such as collisions and for objects separating under internal forces. A collision model compares states immediately before and after an interaction; it does not require the complicated contact force at every instant to be known.
A worked example, step by step
A 0.5 kg puck has velocity (6, −8) m/s. Calculate its momentum vector and magnitude.
- Use the given x and y axes, with the same inertial frame for both components.
- pₓ = (0.5)(6) = +3 kg·m/s and pᵧ = (0.5)(−8) = −4 kg·m/s.
- The vector is p = (3, −4) kg·m/s. Its magnitude is √(3² + 4²) = 5 kg·m/s.
- Momentum points in the same direction as velocity because multiplication by positive mass changes length, not direction.
Do not replace a signed velocity with its speed when momentum direction matters.
Can pₓ be zero while total momentum is nonzero?
Compare with an explanation
Yes. The object may have momentum along y even when its x component is zero.
Predict. Change one thing. Explain.
Keep mass fixed. Change vₓ through zero while holding vᵧ fixed. Predict the momentum components, then compare the arrow with its labeled component values.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
p = (6, 0) kg·m/s; magnitude 6 kg·m/s. Dashed lines project this one momentum vector; they are not additional momenta.
One point object in a fixed inertial frame. Momentum components use the same kg·m/s scale. Axes are momentum axes, not spatial positions.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant impulse, system boundary, momentum or calculus relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA 2 kg object has velocity (−3, 4) m/s. Find both momentum components, its magnitude and explain what the signs tell you.
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Compare with the answer and four-point rubric
- 1 point: pₓ = −6 kg·m/s.
- 1 point: pᵧ = +8 kg·m/s.
- 1 point: |p| = √(36 + 64) = 10 kg·m/s.
- 1 point: The object moves in negative x and positive y; the momentum arrow has the same direction as velocity.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What is the unit of momentum?
kg·m/s, equivalent to N·s.
RECALL 2What makes momentum a vector?
It follows velocity’s direction and combines component by component.
RECALL 3What does negative one-dimensional momentum mean?
Motion along the chosen negative axis.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Momentum carries the direction of motion
- p = mv; momentum unit: kg·m/s.
- pₓ = mvₓ and pᵧ = mvᵧ.
- |p| = m|v| = √(pₓ² + pᵧ²) in a plane.
Remember: Do not replace a signed velocity with its speed when momentum direction matters.
Conditions: One point object in a fixed inertial frame. Momentum components use the same kg·m/s scale. Axes are momentum axes, not spatial positions.
Refresh Kid · AP Physics C: Mechanics Unit 4 (official Unit 4) · Objectives 4.1.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 4.1, objectives 4.1.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026 alongside the Fall 2026 clarifications. This is Mechanics Unit 4: Linear Momentum. The unit covers Topics 4.1–4.4. Calculus connects force to momentum derivatives and impulse integrals. Collision calculations use one or two dimensions; the optional spatial fragment diagram is qualitative. Changing-mass examples explicitly account for momentum carried across a boundary, so dp/dt is not used blindly for an open system. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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