What do I need to know for AP Physics 1 Topic 5.6?
Topic 5.6 Newton’s Second Law in Rotational Form: Newton’s second law for rotation states that the net external torque on a rigid system equals its rotational inertia times angular acceleration.
- Relate torque, rotational inertia, and angular acceleration; connect force diagrams to torque equations; and analyze systems with both translation and rotation.
- 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.
Newton’s Second Law in Rotational Form
Newton’s second law for rotation states that the net external torque on a rigid system equals its rotational inertia times angular acceleration.
Newton’s second law for rotation states that the net external torque on a rigid system equals its rotational inertia times angular acceleration.
What you need to understand before calculating
Relate torque, rotational inertia, and angular acceleration; connect force diagrams to torque equations; and analyze systems with both translation and rotation.
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.
Net torque
Net external torque is the rotational cause of angular acceleration, just as net external force causes translational acceleration.
Real example: The same wheel accelerates angularly more when the applied net torque is larger.
Deeper lesson: Net torqueAngular acceleration
Angular acceleration is the signed rate of change of angular velocity.
Real example: A fan speeding up counterclockwise has positive angular acceleration if counterclockwise is positive.
Deeper lesson: Angular accelerationTranslate 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 |
|---|---|---|---|
| Net torque causes angular acceleration | A nonzero net torque changes angular velocity. | Pushing a door produces angular acceleration. | A motor torque speeds up a flywheel. |
| Rotational inertia resists angular acceleration | For the same net torque, larger I means smaller α. | A loaded flywheel spins up more slowly than a light disk under the same torque. | Extending masses outward reduces angular acceleration for fixed torque. |
| Multiple torques | Use signed sum of all external torques. | Motor torque and friction torque oppose each other. | Two applied forces can create competing clockwise/counterclockwise effects. |
| Translation plus rotation | A rigid body can have center-of-mass acceleration and angular acceleration simultaneously. | A rolling wheel accelerates forward while speeding up its rotation. | A falling spool can translate and rotate due to tension/gravity. |
| External torque on system | Internal torque pairs do not change total angular momentum of a suitably chosen system; rotational dynamics use net external torque. | For a wheel+axle system, bearing friction is external if the support is outside. | For a two-body system, mutual forces can be internal. |
Equations and relationships: variables, units, conditions, examples
| Relationship | Variables & SI units | When to use it | Real example |
|---|---|---|---|
| Στ_ext = Iα | τ: N·m; I: kg·m²; α: rad/s²All symbols used here: τ_net = net external torque (N·m); I = rotational inertia (kg·m²); α = angular acceleration (rad/s²); r = distance from axis (m); F = force (N); θ = angle between r and F. | Rigid-body rotational dynamics about a fixed axis. | 12 N·m on I=3 gives α=4 rad/s². |
| ΣF_ext = Ma_cm | F: N; M: kg; a: m/s²All symbols used here: τ_net = net external torque (N·m); I = rotational inertia (kg·m²); α = angular acceleration (rad/s²); r = distance from axis (m); F = force (N); θ = angle between r and F. | Use alongside rotation when center of mass translates. | Rolling object down ramp needs both translation and rotation equations. |
| τ = rF sinθ | N·mAll symbols used here: τ_net = net external torque (N·m); I = rotational inertia (kg·m²); α = angular acceleration (rad/s²); r = distance from axis (m); F = force (N); θ = angle between r and F. | Convert applied forces to torque. | A perpendicular force at larger r gives greater τ. |
Worked physical reasoning
Flywheel
Situation: A constant motor torque acts on a flywheel.
Physics: α=τ/I; adding rim mass increases I and reduces α.
Door
Situation: Same push force applied near hinge vs handle.
Physics: Handle gives larger torque and therefore larger angular acceleration.
Rolling cylinder
Situation: A cylinder rolls down an incline without slipping.
Physics: Gravity drives translation; static friction provides torque needed for rotation depending on chosen model.
AP scope and boundary
Topic 5.6 completes rotational dynamics; rotational energy and angular momentum are Unit 6.
Common mistakes—and the corrected physics
| Incorrect idea | Correct understanding |
|---|---|
| Net torque determines angular velocity directly. | It determines angular acceleration. |
| Same torque gives same α for all objects. | α depends inversely on I. |
| Use Στ=Iα without specifying an axis. | Torque and rotational inertia are axis-dependent; specify the axis/model. |
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
- Relate net external torque to angular acceleration through rotational inertia.
- Apply Στ = Iα about a suitable fixed axis for the modeled rigid body/system.
- Predict how changing torque or rotational inertia changes angular acceleration.
- Combine rotational and translational equations when a system includes both types of motion.
Must-not-miss relationship
Στ_ext = Iα is the rotational analogue of ΣF_ext = Ma_cm. Torque and rotational inertia together determine angular acceleration.
Symbols & SI units used on this topic: τ_net = net external torque (N·m); I = rotational inertia (kg·m²); α = angular acceleration (rad/s²); r = distance from axis (m); F = force (N); θ = angle between r and F.
Two anchor situations
The same motor torque produces less angular acceleration when masses are moved farther from the axis and I increases.
A hanging mass driving a pulley can require simultaneous translational equations for the mass and a torque equation for the pulley.
Diagram / graph / equation / claim
Pair an FBD with a rotational diagram: identify each torque contribution, write Στ, then predict α’s sign before arithmetic.
How to test the physics
Apply a near-constant torque to a rotational apparatus with two different inertias and compare measured angular accelerations to the predicted inverse relation.
Use one clearly chosen axis and consistent sign convention. Do not treat “Iα” as a physical torque arrow on the diagram.
Carry the torque model into rotational work, angular impulse and angular momentum in Unit 6.
Connect to Topic 6.3 angular impulseGo 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
Sum external torques about a specified axis, determine I about that same axis, then use τ_net=Iα.
Why the physics works
Rotational inertia plays the role of resistance to angular acceleration just as mass resists translational acceleration.
Solve this before opening the solution
A rigid body has I=2.0 kg·m² and experiences a net torque of 6.0 N·m. Find angular acceleration.
Reveal complete reasoning
Solution: α=τ_net/I=6/2=3 rad/s² in the direction of the net torque.
Physics check: Larger I at the same torque would produce smaller α.
What should you plot?
At fixed I, plot angular acceleration α versus net torque τ_net.
What does the graph mean?
The slope is 1/I; comparing slopes reveals rotational inertia.
How this exact topic can appear in each current FRQ mode
Στ_ext = Iα is the rotational analogue of ΣF_ext = Ma_cm. Torque and rotational inertia together determine angular acceleration.
Pair an FBD with a rotational diagram: identify each torque contribution, write Στ, then predict α’s sign before arithmetic.
Apply a near-constant torque to a rotational apparatus with two different inertias and compare measured angular accelerations to the predicted inverse relation.
Carry the torque model into rotational work, angular impulse and angular momentum in Unit 6.
Use torques and I about the same axis, preserve rotational sign, and do not substitute a single applied torque for net torque without justification.
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 5.6 quick review
What is the definition I should know first?
Newton’s second law for rotation states that the net external torque on a rigid system equals its rotational inertia times angular acceleration.
What should I identify before using an equation?
Relate torque, rotational inertia, and angular acceleration; connect force diagrams to torque equations; and analyze systems with both translation and rotation.
Where do I practice this exact topic?
Use the 42-MCQ and 4-FRQ Topic 5.6 banks linked directly on this page.
Where Topic 5.6 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.
Falling block, pulley and angular acceleration
Connects linear acceleration, torque and rotational Newton’s second law.
Mathematical RoutinesRolling wheel, ramp and rotational dynamics
Direct connection to rolling, torque and linear-angular relationships.
Mathematical RoutinesRecent 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.