---
title: "AP Physics 1 Unit 6 Review: Rotational Energy & Momentum"
description: "AP Physics 1 Unit 6 covers Rotational Kinetic Energy and Torque and Work. Study guides, practice questions, and key terms for every topic."
canonical: "https://fiveable.me/ap-physics-1-revised/unit-6"
type: "unit"
subject: "AP Physics 1"
unit: "Unit 6 – Rotating Systems: Energy & Momentum"
---

# AP Physics 1 Unit 6 Review: Rotational Energy & Momentum

## Overview

Unit 6 applies energy and momentum conservation to rotating systems. You will calculate rotational kinetic energy using K = 1/2 I omega squared, find work done by torques using W = tau delta theta, and analyze angular momentum and angular impulse. Conservation of angular momentum explains phenomena from spinning skaters to orbiting satellites, and rolling motion combines translational and rotational kinetic energy.

## AP CED Alignment

This unit hub is organized around AP Course and Exam Description topics, skills, and exam task types when they are available in the source data.
- Topic 6.1: Rotational Kinetic Energy
- Topic 6.2: Torque and Work
- Topic 6.3: Angular Momentum and Angular Impulse
- Topic 6.4: Conservation of Angular Momentum
- Topic 6.5: Rolling
- Topic 6.6: Motion of Orbiting Satellites
- Topic 6.5: Rolling Motion
- Science Practice 3: Scientific Questioning and Argumentation
- Science Practice 2: Mathematical Routines
- FRQ 3 – Experimental Design
- FRQ 2 – Translation Between Representations
- FRQ 1 – Mathematical Routines

## Topics

- [Topic 6.1: Rotational Kinetic Energy](/ap-physics-1-revised/unit-6/1-rotational-kinetic-energy/study-guide/OM0z7GYjhkcWoIlZ): Spinning systems store energy described by K = 1/2 I omega squared. Total kinetic energy for a rolling or rotating-and-translating object is the sum of rotational and translational parts.
- [Topic 6.2: Torque and Work](/ap-physics-1-revised/unit-6/2-torque-and-work/study-guide/D8FrXUDk7DwXDsEZ): Torque does work W = tau delta theta when it acts through an angular displacement. Variable-torque work is the area under a torque-versus-angular-position graph.
- [Topic 6.3: Angular Momentum and Angular Impulse](/ap-physics-1-revised/unit-6/3-angular-momentum-and-angular-impulse/study-guide/SSARCXdw55Twhoxd): Angular momentum is L = I omega for rigid systems or L = rmv sin theta for point objects. Angular impulse tau delta t equals the change in angular momentum, mirroring the linear impulse-momentum theorem.
- [Topic 6.4: Conservation of Angular Momentum](/ap-physics-1-revised/unit-6/4-conservation-of-angular-momentum/study-guide/uWUv9Ei9tpPYbvI9): When net external torque is zero, total angular momentum is conserved. System selection determines whether angular momentum changes, and nonrigid systems can change angular speed by redistributing mass.
- [Topic 6.5: Rolling](/ap-physics-1-revised/unit-6/5-rolling/study-guide/Ezw0DtDmEDYrpqzr): Rolling without slipping links translational and rotational motion via v_cm = r omega. Total kinetic energy is the sum of both parts. Slipping breaks this link and kinetic friction dissipates energy.
- [Topic 6.6: Motion of Orbiting Satellites](/ap-physics-1-revised/unit-6/6-motion-of-orbiting-satellites/study-guide/tzB1DCcspZo8vXIC): Satellite orbits are governed by conservation of energy and angular momentum. Circular orbits have constant speed and energy; elliptical orbits have constant total energy and angular momentum but varying KE and PE.

## Hardest Topics And Analytics

Snapshot: practice snapshot
This snapshot uses Fiveable practice activity to show where students tend to miss questions and which review moves are worth prioritizing first.
- **56% average MCQ accuracy** (Across 4.8k multiple-choice practice attempts for this unit.)
- **4.8k MCQ attempts** (Practice activity included in this snapshot.)
- **56% average FRQ score** (Across 13 scored free-response attempts for this unit.)
- **Topic 6.6: Motion of Orbiting Satellites**: 53% MCQ miss rate across 762 attempts. Review Motion of Orbiting Satellites with attention to how the concept appears in AP-style source and evidence questions.
- **Topic 6.3: Angular Momentum and Angular Impulse**: 49% MCQ miss rate across 885 attempts. Review Angular Momentum and Angular Impulse with attention to how the concept appears in AP-style source and evidence questions.
- **Topic 6.1: Rotational Kinetic Energy**: 47% MCQ miss rate across 884 attempts. Review Rotational Kinetic Energy with attention to how the concept appears in AP-style source and evidence questions.
- **Topic 6.2: Torque and Work**: 39% MCQ miss rate across 691 attempts. Review Torque and Work with attention to how the concept appears in AP-style source and evidence questions.

## Review Notes

### Topic 6.1: Rotational Kinetic Energy

A spinning rigid system has rotational kinetic energy given by K = 1/2 I omega squared, where I is the rotational inertia and omega is the angular velocity. This is a scalar quantity. When an object both translates and rotates, total kinetic energy is the sum of translational and rotational parts: K_tot = 1/2 M v_cm squared + 1/2 I_cm omega squared. A rigid system can have rotational kinetic energy even when its center of mass is stationary, because individual points within the system still have linear speed.

- **K = 1/2 I omega squared**: Rotational kinetic energy of a rigid system; depends on both how mass is distributed (I) and how fast it spins (omega).
- **Total KE decomposition**: K_tot = K_trans + K_rot = 1/2 M v_cm squared + 1/2 I_cm omega squared; applies to any object with both translational and rotational motion.
- **Rotational inertia I**: Measures how mass is distributed relative to the rotation axis; larger I means more energy stored at the same omega.
- **Scalar quantity**: Rotational kinetic energy has magnitude only, no direction, just like translational kinetic energy.

**Checkpoint:** A solid disk and a thin ring have the same mass and radius. Which stores more rotational kinetic energy at the same angular velocity, and why?

Quantity | Translational form | Rotational form
--- | --- | ---
Kinetic energy | K = 1/2 m v squared | K = 1/2 I omega squared
Inertia | mass m | rotational inertia I
Speed | v (linear) | omega (angular)

### Topic 6.2: Torque and Work

A torque transfers energy into or out of a rotating system when it acts through an angular displacement. The work done by a constant torque is W = tau delta theta, where theta is measured in radians. For a variable torque, work equals the area under the torque-versus-angular-position graph. This is the rotational analog of W = F delta x from Unit 3.

- **W = tau delta theta**: Work done by a torque acting through angular displacement delta theta; theta must be in radians.
- **Area under torque-angle graph**: For variable torque, the work done equals the area under the curve of torque versus angular position.
- **Energy transfer direction**: A torque in the same direction as angular displacement does positive work (adds energy); opposite direction does negative work (removes energy).
- **Work-energy theorem for rotation**: Net work done by all torques equals the change in rotational kinetic energy of the system.

**Checkpoint:** A torque of 4 N m acts on a wheel through an angular displacement of pi/2 radians. How much work is done on the wheel?

Concept | Linear version | Rotational version
--- | --- | ---
Work formula | W = F delta x | W = tau delta theta
Variable-force work | Area under F-x graph | Area under tau-theta graph
Work-energy theorem | W_net = delta KE_trans | W_net = delta KE_rot

### Topic 6.3: Angular Momentum and Angular Impulse

Angular momentum quantifies how much rotational motion a system has. For a rigid system rotating about an axis, L = I omega. For a point object moving about a reference point, L = rmv sin theta, where theta is the angle between the radial distance and the velocity. The choice of reference axis affects the calculated value of L. Angular impulse equals tau times delta t and produces a change in angular momentum: delta L = tau delta t. This is the rotational impulse-momentum theorem. On a torque-versus-time graph, the area under the curve equals the angular impulse delivered.

- **L = I omega**: Angular momentum of a rigid system; depends on rotational inertia and angular velocity.
- **L = rmv sin theta**: Angular momentum of a point object about a reference point; theta is the angle between r and v.
- **Angular impulse = tau delta t**: The product of net torque and time interval; equals the change in angular momentum of the system.
- **delta L = tau delta t**: Rotational impulse-momentum theorem; angular impulse equals change in angular momentum.
- **Torque-time graph**: The area under a torque-versus-time graph gives the angular impulse delivered to the system.

**Checkpoint:** A net torque of 3 N m acts on a flywheel for 2 seconds. What is the change in angular momentum of the flywheel?

Quantity | Linear form | Rotational form
--- | --- | ---
Momentum | p = mv | L = I omega
Impulse | J = F delta t | angular impulse = tau delta t
Impulse-momentum theorem | delta p = F delta t | delta L = tau delta t
Graph interpretation | Area under F-t = impulse | Area under tau-t = angular impulse

### Topic 6.4: Conservation of Angular Momentum

The total angular momentum of a system is the sum of the angular momenta of its parts. If the net external torque on a chosen system is zero, total angular momentum is constant. If net external torque is nonzero, angular momentum is transferred between the system and its surroundings. A nonrigid system can change its angular speed without any external torque if it redistributes mass, changing its moment of inertia. The classic example is a spinning skater who pulls her arms in, decreasing I and increasing omega to keep L constant. System selection determines whether angular momentum is conserved.

- **Conservation condition**: Angular momentum is conserved when net external torque on the chosen system is zero.
- **System selection**: Choosing which objects to include in your system determines whether angular momentum changes or stays constant.
- **Nonrigid system**: A system that can change shape, redistributing mass and changing I, so omega changes even with no external torque.
- **L_initial = L_final**: When angular momentum is conserved: I_1 omega_1 = I_2 omega_2.
- **Newton's third law connection**: Angular impulses between two interacting objects are equal and opposite, so internal torques cannot change total system angular momentum.

**Checkpoint:** A student sits on a frictionless rotating stool holding weights at arm's length. She pulls the weights to her chest. Describe what happens to her angular velocity and why.

Condition | Angular momentum | Example
--- | --- | ---
Net external torque = 0 | Conserved (constant) | Skater pulling arms in
Net external torque nonzero | Changes; transferred to/from environment | Torque applied by braking force
Internal torques only | No change to total L | Two parts of a system pushing on each other

### Topic 6.5: Rolling Motion

Rolling combines translational motion of the center of mass with rotation about that center. When rolling without slipping, the no-slip condition links the two motions: v_cm = r omega, a_cm = r alpha, and delta x_cm = r delta theta. Total kinetic energy is K_tot = 1/2 M v_cm squared + 1/2 I omega squared. Static friction enables rolling without slipping but does no work and dissipates no energy. When slipping occurs, kinetic friction acts, the no-slip condition breaks down, and energy is dissipated as heat.

- **No-slip condition**: v_cm = r omega; links the translational speed of the center of mass to the angular velocity when rolling without slipping.
- **K_tot = K_trans + K_rot**: Total kinetic energy of a rolling object is the sum of translational and rotational kinetic energies.
- **Static friction in rolling**: Provides the torque needed to maintain rolling without slipping; does no work and dissipates no energy.
- **Rolling while slipping**: When slipping, v_cm and r omega are not equal; kinetic friction acts and dissipates energy from the system.
- **Effect of shape on rolling speed**: Objects with more mass concentrated near the rim (larger I) roll more slowly down a ramp than objects with mass near the center.

**Checkpoint:** A solid sphere and a hollow sphere of equal mass and radius roll from rest down the same ramp. Which reaches the bottom first, and what principle explains the difference?

Condition | v_cm vs r omega | Friction type | Energy dissipated?
--- | --- | --- | ---
Rolling without slipping | v_cm = r omega | Static | No
Rolling while slipping | v_cm not equal to r omega | Kinetic | Yes

### Topic 6.6: Motion of Orbiting Satellites

When a satellite's mass is negligible compared to the central body, the central body's motion is ignored. Satellite orbits are governed by conservation of energy and angular momentum. In a circular orbit, total mechanical energy, gravitational potential energy, kinetic energy, and angular momentum are all constant. In an elliptical orbit, total mechanical energy and angular momentum remain constant, but kinetic energy and gravitational potential energy trade off as the satellite moves closer to or farther from the central body. Gravitational potential energy is defined as U_g = -G m_1 m_2 / r, with zero at infinite separation. Escape velocity is the speed at which total mechanical energy equals zero.

- **Circular orbit**: Speed, kinetic energy, gravitational potential energy, and angular momentum are all constant throughout the orbit.
- **Elliptical orbit**: Total mechanical energy and angular momentum are constant; kinetic energy and gravitational potential energy vary as the satellite moves.
- **U_g = -G m_1 m_2 / r**: Gravitational potential energy; negative and defined as zero at infinite separation.
- **Escape velocity**: v_esc = sqrt(2GM/r); the speed at which total mechanical energy of the satellite-planet system equals zero.
- **Conservation of angular momentum in orbits**: A satellite moves fastest at closest approach (periapsis) and slowest at farthest point (apoapsis) to conserve L = rmv sin theta.

**Checkpoint:** A satellite in an elliptical orbit is at its closest point to Earth. Compared to its farthest point, is its speed greater, smaller, or the same? Which conservation law explains this?

Orbit type | Total mechanical energy | Angular momentum | KE and PE
--- | --- | --- | ---
Circular | Constant | Constant | Both constant
Elliptical | Constant | Constant | Both vary (trade off)

## Study Guides

- [6.1 Rotational Kinetic Energy](/ap-physics-1-revised/unit-6/1-rotational-kinetic-energy/study-guide/OM0z7GYjhkcWoIlZ)
- [6.2 Torque and Work](/ap-physics-1-revised/unit-6/2-torque-and-work/study-guide/D8FrXUDk7DwXDsEZ)
- [6.3 Angular Momentum and Angular Impulse](/ap-physics-1-revised/unit-6/3-angular-momentum-and-angular-impulse/study-guide/SSARCXdw55Twhoxd)
- [6.4 Conservation of Angular Momentum](/ap-physics-1-revised/unit-6/4-conservation-of-angular-momentum/study-guide/uWUv9Ei9tpPYbvI9)
- [6.5 Rolling](/ap-physics-1-revised/unit-6/5-rolling/study-guide/Ezw0DtDmEDYrpqzr)
- [6.6 Motion of Orbiting Satellites](/ap-physics-1-revised/unit-6/6-motion-of-orbiting-satellites/study-guide/tzB1DCcspZo8vXIC)

## Practice Preview

### Multiple-choice practice

- **Stimulus-based practice question**: Science Practice 3: Scientific Questioning and Argumentation | Which choice best evaluates the student's claim?
- **Stimulus-based practice question**: Science Practice 2: Mathematical Routines | Which of the following is most nearly the angular speed of the wheel at $t = 4.0 \text{ s}$?
- **Stimulus-based practice question**: Science Practice 2: Mathematical Routines | What is the magnitude of the tangential force applied to the disk?
- **Stimulus-based practice question**: Science Practice 2: Mathematical Routines | If the forces are applied for $2.0 \text{ s}$, what is the magnitude of the final angular momentum of the rod?
- **Stimulus-based practice question**: Science Practice 2: Mathematical Routines | How much time does it take for the platform to come to a complete stop?
- **Stimulus-based practice question**: Science Practice 3: Scientific Questioning and Argumentation | Which expression represents the total work done on the flywheel by the motor during the total angular displacement $2\theta_0$ ?

### FRQ practice

- **Rotational inertia determination through torque and angular acceleration**: FRQ 3 – Experimental Design | Rotational inertia determination through torque and angular acceleration
- **Rotating disk with falling block energy conversion**: FRQ 2 – Translation Between Representations | Rotating disk with falling block energy conversion
- **Rotating disk-ring system angular momentum behavior**: FRQ 1 – Mathematical Routines | Rotating disk-ring system angular momentum behavior

## Key Terms

- **rigid system**: A system that holds its shape but in which different points move in different directions during rotation; cannot be modeled as a single point object.
- **axis of rotation**: The specified line about which a rigid system rotates; the choice of axis affects calculated values of angular momentum and rotational inertia.
- **scalar**: A physical quantity described by magnitude only; rotational kinetic energy is a scalar, just like translational kinetic energy.
- **impulse-momentum theorem**: In rotational form: angular impulse (tau delta t) equals the change in angular momentum (delta L), directly paralleling the linear version.
- **elliptical orbit**: An orbital path in which a satellite's distance from the central object varies; total mechanical energy and angular momentum are constant, but kinetic energy and gravitational potential energy each change.
- **escape velocity**: The minimum speed needed for a satellite to escape a central object's gravity; at this speed, total mechanical energy of the system equals zero. v_esc = sqrt(2GM/r).
- **Mass independence of orbital period**: The orbital period of a satellite depends only on the orbital radius and the mass of the central body, not on the satellite's own mass.

## Common Mistakes

- **Forgetting to include both KE terms for rolling objects**: When a ball or cylinder rolls, total kinetic energy is K_trans + K_rot. Using only 1/2 mv squared ignores the rotational contribution and gives the wrong answer for speed or energy comparisons.
- **Using degrees instead of radians in rotational work**: The formula W = tau delta theta requires angular displacement in radians. Converting to degrees before plugging in will produce an incorrect result.
- **Assuming angular momentum is always conserved**: Angular momentum is conserved only when net external torque on the chosen system is zero. If an external torque acts, angular momentum changes. Always check your system boundary before applying conservation.
- **Confusing the two angular momentum formulas**: L = I omega applies to a rigid system rotating about an axis. L = rmv sin theta applies to a point object about a reference point. Using the wrong formula, especially when the object moves in a straight line, leads to errors.
- **Treating elliptical and circular orbits the same**: In a circular orbit, speed and both energy terms are constant. In an elliptical orbit, only total mechanical energy and angular momentum are constant; kinetic energy and gravitational potential energy both change as the satellite moves.

## Exam Connections

- **Conservation law reasoning across scenarios**: AP Physics 1 questions in this unit frequently ask you to identify which quantities are conserved in a given scenario and explain why. You may need to compare a system before and after an interaction, such as a mass landing on a rotating disk or a satellite moving between orbital positions, and justify your answer using conservation of energy or angular momentum.
- **Graph interpretation for rotational quantities**: Expect questions that present torque-versus-time or torque-versus-angular-position graphs and ask you to extract angular impulse or work from the area under the curve. You may also be asked to interpret the slope of an angular-momentum-versus-time graph as net torque.
- **Qualitative and quantitative system analysis**: Free-response questions often ask you to both calculate a quantity (such as angular velocity after a collision or speed at a point in an elliptical orbit) and explain the physics in words. Connecting the formula to the underlying principle, such as why a skater spins faster or why a satellite speeds up at closest approach, is a key skill tested in this unit.

## Final Review Checklist

- **Calculate rotational kinetic energy**: Apply K = 1/2 I omega squared to a spinning rigid system and K_tot = K_trans + K_rot to a system with both translational and rotational motion.
- **Find work done by a torque**: Use W = tau delta theta for constant torque and read the area under a torque-versus-angular-position graph for variable torque.
- **Calculate angular momentum two ways**: Use L = I omega for rigid systems rotating about an axis and L = rmv sin theta for a point object about a reference point. Know how axis choice affects the result.
- **Apply the rotational impulse-momentum theorem**: Relate angular impulse (tau delta t) to change in angular momentum (delta L). Interpret the area under a torque-versus-time graph as angular impulse.
- **Use conservation of angular momentum**: Identify whether net external torque is zero, select your system, and set I_1 omega_1 = I_2 omega_2 for nonrigid systems that change shape.
- **Analyze rolling motion**: Apply v_cm = r omega for rolling without slipping, compute total kinetic energy as the sum of translational and rotational parts, and distinguish static friction (no energy loss) from kinetic friction (energy dissipated).
- **Apply conservation laws to satellite orbits**: Distinguish circular orbits (all quantities constant) from elliptical orbits (total energy and angular momentum constant; KE and PE vary). Use U_g = -Gm_1m_2/r and the escape velocity condition.

## Study Plan

- **Start with rotational kinetic energy and work (Topics 6.1-6.2)**: Read the Topic 6.1 and 6.2 guides on Fiveable. Practice writing K = 1/2 I omega squared and W = tau delta theta, and work through problems that ask you to find total kinetic energy for spinning or rolling objects. Sketch a torque-versus-angle graph and identify the area as work.
- **Build angular momentum and impulse skills (Topic 6.3)**: Study the Topic 6.3 guide and practice applying both L = I omega and L = rmv sin theta to different scenarios. Work problems that use delta L = tau delta t and practice reading angular impulse from a torque-versus-time graph.
- **Practice conservation of angular momentum (Topic 6.4)**: Use the Topic 6.4 guide to work through system-selection problems. For each scenario, identify whether net external torque is zero, then apply I_1 omega_1 = I_2 omega_2. Try the spinning skater and rotational collision examples.
- **Work through rolling motion problems (Topic 6.5)**: Review the Topic 6.5 guide and practice problems that combine v_cm = r omega with energy conservation. Compare rolling without slipping to rolling while slipping, and identify when friction dissipates energy.
- **Finish with satellite orbits and review the full unit (Topic 6.6)**: Study the Topic 6.6 guide, focusing on what stays constant in circular versus elliptical orbits. Then do a full unit review using available practice questions and the AP score calculator on Fiveable to estimate your readiness.

## More Ways To Review

- [Topic study guides](/ap-physics-1-revised/unit-6#topics)
- [FRQ practice](/ap-physics-1-revised/frq-practice)
- [Cram archive videos](/cram-archives?subject=ap-physics-1-revised&unit=unit-6)
- [Key terms](/ap-physics-1-revised/key-terms)

## FAQs

### What topics are covered in AP Physics 1 Unit 6?

AP Physics 1 Unit 6 covers work and energy in rotating systems across 6 topics: Rotational Kinetic Energy (6.1), Torque and Work (6.2), Angular Momentum and Angular Impulse (6.3), Conservation of Angular Momentum (6.4), Rolling (6.5), and Motion of Orbiting Satellites (6.6). Together these topics apply energy and momentum principles to spinning and orbiting objects. See the full topic list and practice at [/ap-physics-1-revised/unit-6](/ap-physics-1-revised/unit-6).

### How much of the AP Physics 1 exam is Unit 6?

Unit 6 makes up 5-8% of the AP Physics 1 exam. That slice covers rotating systems, including work done by torque, rotational kinetic energy, angular momentum, angular impulse, and the motion of orbiting satellites. It's a smaller unit by weight, but the concepts connect directly to the larger mechanics picture tested throughout the exam.

### What's on the AP Physics 1 Unit 6 progress check (MCQ and FRQ)?

The AP Physics 1 Unit 6 progress check includes both MCQ and FRQ parts drawn from all six unit topics: rotational kinetic energy, torque and work, angular momentum, angular impulse, conservation of angular momentum, rolling, and orbiting satellites. MCQ questions typically ask you to apply or compare these concepts, while the FRQ part asks you to justify reasoning about energy and momentum in rotating systems. For matched practice that mirrors the progress check format, visit [/ap-physics-1-revised/unit-6](/ap-physics-1-revised/unit-6).

### How do I practice AP Physics 1 Unit 6 FRQs?

AP Physics 1 Unit 6 FRQs most often come from torque and work, conservation of angular momentum, and rolling, since those topics require multi-step reasoning and written justification. Expect questions that ask you to calculate work done by a torque, explain why angular momentum is conserved, or analyze a rolling object's energy. Practice by writing out full solution steps and explaining your reasoning in words, not just equations. Find Unit 6 FRQ practice at [/ap-physics-1-revised/unit-6](/ap-physics-1-revised/unit-6).

### Where can I find AP Physics 1 Unit 6 practice questions?

The best place to find AP Physics 1 Unit 6 practice questions, including multiple-choice and practice test sets, is [/ap-physics-1-revised/unit-6](/ap-physics-1-revised/unit-6). That page has MCQ and FRQ practice covering all six topics: rotational kinetic energy, torque, work, angular momentum, impulse, rolling, and orbiting satellites. Working through topic-by-topic MCQs before taking a full practice test helps you spot which concepts need more attention.

### How should I study AP Physics 1 Unit 6?

Start with rotational kinetic energy and torque so you have a solid foundation before tackling angular momentum and angular impulse. Those two concepts build on each other the same way linear momentum and impulse do, so the comparison helps. Then work through conservation of angular momentum with concrete examples like a spinning skater pulling in their arms. Rolling is tricky because it mixes translational and rotational energy, so practice splitting the kinetic energy into both parts. Finish with orbiting satellites, connecting orbital motion back to energy conservation. Practice problems and topic guides for each step are at [/ap-physics-1-revised/unit-6](/ap-physics-1-revised/unit-6).

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