A straight-moving object can have angular momentum
You will be able to: Use the perpendicular distance to a particle’s line of motion to calculate angular momentum.
Can a puck sliding straight past you have angular momentum about you?
A puck slides in a straight line past a marked point on a table. Although its path does not curve, the line from the marked point to the puck changes angle. The puck has angular momentum about that point if its line of motion misses the point.
A useful starting point: Angular momentum of a rigid system →
Words and symbols before equations
- Reference point
- The point about which angular momentum is measured.
- r and φ
- Distance from the reference point to the particle, and angle between that radius and velocity.
- Impact parameter b
- Perpendicular distance from reference point to the straight line of motion, in m.
- Linear momentum p
- Mass times velocity; magnitude mv, in kg·m/s.
What this picture assumes
Top view. A 2 kg puck moves right at 3 m/s on a horizontal track. CCW positive about O. Length scale: 80 drawing units per meter. Velocity arrow has fixed length.
Connect the picture to the physics
The magnitude is L=rmv sinφ. The perpendicular distance b=r sinφ gives the simpler expression |L|=mvb for a straight path. Only the part of motion perpendicular to the radius contributes.
Move the puck along a fixed straight track at constant speed. r and φ change together, but b stays the same, so angular momentum about the marked point stays constant. Do not conclude that larger r always means larger L when the angle is also changing.
Choosing a reference point on the track gives b=0 and zero L about that point. A different point can give nonzero L for the same motion. In our top view, a puck moving right above the origin has a clockwise, negative signed L under the CCW-positive convention.
A worked example, step by step
A 2 kg puck moves right at 3 m/s along a track 0.5 m above a reference point. Find angular momentum about that point and about a point on the track.
- The perpendicular distance to the first reference point is b=0.5 m.
- |L|=mvb=(2)(3)(0.5)=3 kg·m²/s.
- Its clockwise tendency about that point gives L=−3 kg·m²/s with CCW positive.
- For a point on the track, b=0, so L=0. The puck itself has not changed motion.
A particle need not travel in a circle to have angular momentum. Specify the reference point.
A particle travels straight toward the reference point. What is L about that point?
Compare with an explanation
Zero: the motion is radial, so the perpendicular distance to the line of motion is zero.
Predict. Change one thing. Explain.
Change the track’s height above the origin, then move the puck along the track. Notice which change alters b and L. The diagram uses one length scale; the arrow marks rightward velocity.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
The track is 0.5 m above O. r=1.12 m; |L|=mvb=3 kg·m²/s; signed L=-3 kg·m²/s. Moving along the same track leaves L unchanged.
Top view. A 2 kg puck moves right at 3 m/s on a horizontal track. CCW positive about O. Length scale: 80 drawing units per meter. Velocity arrow has fixed length.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant physical relationship or contact condition 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 0.5 kg puck moves right at 8 m/s on a straight track 2 m above origin O. (a) Identify b. (b) Find |L_O|. (c) State the signed value for CCW positive. (d) Explain whether L_O changes as the puck passes O.
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Compare with the answer and four-point rubric
- 1 point: b=2 m.
- 1 point: |L|=0.5×8×2=8 kg·m²/s.
- 1 point: L=−8 kg·m²/s, clockwise about O.
- 1 point: No, for constant speed: b remains 2 m even as r and the angle change.
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 b in |L|=mvb?
Perpendicular distance to the line of motion.
RECALL 2When is particle L zero about a point?
When the velocity line passes through that point, or the particle has zero momentum.
RECALL 3Can changing the reference point change L?
Yes, even for unchanged motion.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
A straight-moving object can have angular momentum
- |L|=rmv sinφ=mvb.
- For a straight track at constant speed and fixed b, L is constant.
Remember: A particle need not travel in a circle to have angular momentum. Specify the reference point.
Conditions: Top view. A 2 kg puck moves right at 3 m/s on a horizontal track. CCW positive about O. Length scale: 80 drawing units per meter. Velocity arrow has fixed length.
Refresh Kid · Unit 6 · Objectives 6.3.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 6.3, objectives 6.3.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. 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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