What do I need to know for AP Physics 1 Topic 6.5?
Topic 6.5 Rolling: Rolling motion combines translation of an object’s center of mass with rotation about its center; rolling without slipping imposes a geometric constraint between linear and angular motion.
- Distinguish rolling without slipping from rolling while slipping, use v_cm=Rω and a_cm=Rα only for the no-slip case, combine translational and rotational energy, and reason about friction and rolling dynamics.
- Practice target: 42 original MCQs and 4 original FRQs for this exact topic.
- Course alignment: current AP Physics 1 framework for the 2026–27 school year and May 2027 exam.
Rolling
Rolling motion combines translation of an object’s center of mass with rotation about its center; rolling without slipping imposes a geometric constraint between linear and angular motion.
Rolling motion combines translation of an object’s center of mass with rotation about its center; rolling without slipping imposes a geometric constraint between linear and angular motion.
What you need to understand before calculating
Distinguish rolling without slipping from rolling while slipping, use v_cm=Rω and a_cm=Rα only for the no-slip case, combine translational and rotational energy, and reason about friction and rolling dynamics.
This page explains the key vocabulary where it is used. Internal links are for deeper study, not a requirement for understanding the sentence you are reading.
Key terms explained on this page
These terms are defined here before they are used in the calculations. A deeper internal link is optional where one exists; the reader does not need to leave this page to understand the current explanation.
Rolling without slipping
No-slip rolling means the contact point is instantaneously at rest relative to the surface, which gives v_cm=Rω.
Real example: A bicycle tire gripping dry pavement can roll without slipping.
Rolling while slipping
Rolling while slipping means translation and rotation occur together but the contact point slides, so v_cm=Rω is not valid.
Real example: A bowling ball can skid and spin before friction brings it to no-slip rolling.
Deeper lesson: Rolling while slippingTranslate the physics into a representation
AP Physics 1 frequently asks you to move between words, diagrams, graphs and equations. Use this representation as a reasoning anchor, then explain what each labeled quantity means in this topic.
Core concepts with real physical examples
| Concept | Meaning | Real example 1 | Real example 2 |
|---|---|---|---|
| Rolling without slipping | The point of contact is instantaneously at rest relative to the surface for ideal no-slip rolling. | A bicycle tire grips the road without skidding. | A cylinder rolls down a rough-enough incline without slipping. |
| Kinematic constraint | Center-of-mass speed and angular speed satisfy v_cm=Rω. | A wheel of radius 0.5 m rotating at 4 rad/s rolls at 2 m/s. | Larger radius requires lower ω for the same rolling speed. |
| Combined kinetic energy | Rolling object has translational and rotational kinetic energy. | A bowling ball has both ½Mv² and ½Iω². | A hoop and disk at same v can have different total K because I differs. |
| Static friction role | Static friction can supply torque without necessarily dissipating mechanical energy. | A cylinder rolling down an incline may need static friction to set its angular acceleration. | A driven car tire pushes backward on road while road friction pushes tire forward. |
| Rolling while slipping | An object can translate and rotate while the contact point slips relative to the surface; then the no-slip constraint v_cm=Rω does not apply. | A bowling ball initially skids and spins before kinetic friction brings it toward rolling without slipping. | A tire that locks during hard braking rotates too slowly for v_cm=Rω and slides across the road. |
Equations and relationships: variables, units, conditions, examples
| Relationship | Variables & SI units | When to use it | Real example |
|---|---|---|---|
| v_cm = Rω | v: m/s; R: m; ω: rad/sAll symbols used here: v_cm = center-of-mass speed (m/s); R = radius (m); ω = angular speed (rad/s); a_cm = center-of-mass acceleration (m/s²); α = angular acceleration (rad/s²); M = mass (kg); I = rotational inertia (kg·m²); K = kinetic energy (J). | Rolling without slipping. | R=.25 m, ω=8 gives v=2 m/s. |
| a_cm = Rα | a: m/s²; R: m; α: rad/s²All symbols used here: v_cm = center-of-mass speed (m/s); R = radius (m); ω = angular speed (rad/s); a_cm = center-of-mass acceleration (m/s²); α = angular acceleration (rad/s²); M = mass (kg); I = rotational inertia (kg·m²); K = kinetic energy (J). | No-slip rolling angular acceleration relation. | R=.5, α=4 gives a=2 m/s². |
| K = ½Mv_cm² + ½Iω² | K: J; M: kg; v_cm: m/s; I: kg·m²; ω: rad/sAll symbols used here: v_cm = center-of-mass speed (m/s); R = radius (m); ω = angular speed (rad/s); a_cm = center-of-mass acceleration (m/s²); α = angular acceleration (rad/s²); M = mass (kg); I = rotational inertia (kg·m²); K = kinetic energy (J). | Total kinetic energy of a rigid body that both translates and rotates. | Use with energy conservation for a rigid body rolling down a ramp. |
Worked physical reasoning
Bowling ball
Situation: Ball rolls along lane without slipping.
Physics: Its center translates while it rotates; both kinetic-energy terms matter.
Disk down ramp
Situation: Solid disk rolls from rest down incline.
Physics: Gravitational potential energy becomes translational + rotational kinetic energy.
Car tire
Situation: Driven tire accelerates vehicle.
Physics: Static friction at contact can point forward on the driven tire and provide translational force/torque relationship.
AP scope and boundary
AP Physics 1 requires quantitative rolling-without-slipping relationships and qualitative reasoning about rolling while slipping. During slipping, kinetic friction dissipates mechanical energy; quantitative slipping relations between translation and rotation are beyond scope, and rolling resistance is not required.
Common mistakes—and the corrected physics
| Incorrect idea | Correct understanding |
|---|---|
| Rolling automatically means no slipping. | An object can roll while also slipping; no-slip must be stated/justified. |
| Static friction always removes mechanical energy. | Static friction in ideal rolling can do no dissipative work at the instantaneous contact. |
| All shapes roll down a ramp with the same acceleration. | Acceleration depends on rotational inertia distribution. |
Master this topic beyond a formula list
This checkpoint combines the current AP Physics 1 content boundary with representation, experiment/data reasoning, real situations and cross-topic transfer.
2026–27 mastery checklist
- Distinguish rolling without slipping from rolling while slipping by the relative motion at the contact point.
- Use v_cm = Rω (and compatible tangential relations) only for no-slip rolling.
- Combine translational and rotational kinetic energy for a rolling rigid body.
- Explain how static friction can enable no-slip rolling and how kinetic friction during slipping can dissipate mechanical energy.
Must-not-miss relationship
No-slip rolling imposes v_cm = Rω and the contact point is instantaneously at rest relative to the surface. During slipping this constraint is not valid; kinetic friction can transform mechanical energy.
Symbols & SI units used on this topic: v_cm = center-of-mass speed (m/s); R = radius (m); ω = angular speed (rad/s); a_cm = center-of-mass acceleration (m/s²); α = angular acceleration (rad/s²); M = mass (kg); I = rotational inertia (kg·m²); K = kinetic energy (J).
Two anchor situations
A wheel rolling steadily on a road without slipping has a top point moving faster than its center relative to the ground while the contact point is momentarily at rest.
A locked tire skidding during braking is rolling while slipping, so v_cm ≠ Rω and kinetic friction dissipates energy.
Diagram / graph / equation / claim
Draw velocity vectors for the center, top and contact point in no-slip rolling; then contrast with a slipping case where the contact-point velocity is nonzero.
How to test the physics
Roll a cylinder down a ramp and use video to measure v_cm and ω. Test v_cm/Rω and identify when slipping occurs.
Quantitative relationships for rolling while slipping and rolling resistance are beyond the current scope; do not apply the no-slip constraint after slipping begins.
Combine Topic 6.5 with energy conservation and friction concepts from Units 2–3.
Reconnect to Topic 2.7 frictionGo beyond memorizing the equation
This topic now combines model selection, physical intuition, a worked transfer problem, graph/data analysis, answer verification, and the four current AP free-response reasoning modes.
Choose the model before calculating
Determine whether rolling is without slipping. If yes, use v_cm=Rω and a_cm=Rα; then include both translational and rotational kinetic energy. If slipping occurs, the no-slip constraint does not apply.
Why the physics works
No-slip rolling geometrically locks translation to rotation because the contact point is instantaneously at rest relative to the surface.
Solve this before opening the solution
A wheel of radius 0.25 m rolls without slipping at angular speed 8 rad/s. Find center-of-mass speed.
Reveal complete reasoning
Solution: v_cm=Rω=0.25·8=2.0 m/s.
Physics check: A larger radius at the same ω would produce a larger translational speed.
What should you plot?
For verified no-slip trials, plot v_cm versus ω.
What does the graph mean?
The slope is R. Slipping trials fall away from this linear constraint.
How this exact topic can appear in each current FRQ mode
No-slip rolling imposes v_cm = Rω and the contact point is instantaneously at rest relative to the surface. During slipping this constraint is not valid; kinetic friction can transform mechanical energy.
Draw velocity vectors for the center, top and contact point in no-slip rolling; then contrast with a slipping case where the contact-point velocity is nonzero.
Roll a cylinder down a ramp and use video to measure v_cm and ω. Test v_cm/Rω and identify when slipping occurs.
Combine Topic 6.5 with energy conservation and friction concepts from Units 2–3.
State whether the contact condition is no-slip or slipping before using v=Rω, and distinguish static friction from kinetic friction.
Continue with the exact topic question banks
Use the focused banks for skill practice. The five full model papers are reserved for whole-exam simulation.
Topic 6.5 quick review
What is the definition I should know first?
Rolling motion combines translation of an object’s center of mass with rotation about its center; rolling without slipping imposes a geometric constraint between linear and angular motion.
What should I identify before using an equation?
Distinguish rolling without slipping from rolling while slipping, use v_cm=Rω and a_cm=Rα only for the no-slip case, combine translational and rotational energy, and reason about friction and rolling dynamics.
Where do I practice this exact topic?
Use the 42-MCQ and 4-FRQ Topic 6.5 banks linked directly on this page.
Where Topic 6.5 appears in AP-style released work
These are original topic summaries and alignment notes, not reproduced College Board question text. One released FRQ can legitimately connect to several topics.
Rolling wheel, ramp and rotational dynamics
Direct connection to rolling, torque and linear-angular relationships.
Mathematical RoutinesSpinning tops, rotational inertia and rotational energy
Combines rotational inertia, work-energy and qualitative/quantitative comparison.
Qualitative / Quantitative TranslationRecent public FRQs are the safest format reference. Older released questions can still contain excellent physics, but the course and exam changed; use the atlas alignment notes before treating a legacy question as a current-format simulation.