Review AP Physics 1 Unit 6 to build your understanding of how energy and momentum principles extend to rotating systems. From spinning objects and rolling motion to orbiting satellites, this unit connects rotational kinematics with conservation laws.
Use the topic guides, key terms, and practice questions available on Fiveable to work through each concept before your exam.
Unit 6 extends the energy and momentum ideas from Units 3 and 4 into the rotational domain. Every major principle you used for linear motion has a rotational counterpart here: kinetic energy, work, impulse, and momentum all reappear in rotational form.
Unit 6 covers rotational kinetic energy, work done by torques, angular momentum, angular impulse, conservation of angular momentum, rolling motion, and satellite orbits. The core skill is applying conservation laws to systems that spin, roll, or orbit.
Rotational kinetic energy is K = 1/2 I omega squared. Torque does work equal to W = tau delta theta, which you can also read as the area under a torque-versus-angular-position graph. These tools let you track energy in spinning systems the same way you tracked it in linear systems.
Angular momentum is L = I omega for a rigid system or L = rmv sin theta for a point object about a reference point. Angular impulse equals tau times delta t and produces a change in angular momentum, mirroring the linear impulse-momentum theorem.
When net external torque is zero, angular momentum is conserved. This explains why a skater spins faster with arms pulled in and why satellites speed up at closest approach. Rolling without slipping adds a geometric constraint, v_cm = r omega, that links translational and rotational motion.
The most powerful idea in Unit 6 is that angular momentum is conserved whenever net external torque is zero. Whether you are analyzing a spinning figure skater, a rolling ball on a ramp, or a satellite in an elliptical orbit, the same conservation framework applies. Choosing your system carefully determines whether angular momentum changes or stays constant, and that choice drives most of the reasoning on exam questions.
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.
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.
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.
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.
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.
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.
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Review Motion of Orbiting Satellites with attention to how the concept appears in AP-style source and evidence questions.
Review Angular Momentum and Angular Impulse with attention to how the concept appears in AP-style source and evidence questions.
Review Rotational Kinetic Energy with attention to how the concept appears in AP-style source and evidence questions.
Review Torque and Work with attention to how the concept appears in AP-style source and evidence questions.
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.
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) |
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.
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 |
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.
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 |
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.
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 |
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.
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 |
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.
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) |
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A timed, AP-style test built only from unit 6 questions — multiple choice plus free response, scored with AI feedback. Use the standard format or build your own.
| Term | Definition |
|---|---|
| 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. |
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.
The formula W = tau delta theta requires angular displacement in radians. Converting to degrees before plugging in will produce an incorrect result.
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.
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.
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.
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.
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.
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.
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.
Use W = tau delta theta for constant torque and read the area under a torque-versus-angular-position graph for variable torque.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
Open the individual guides for Unit 6 when you want a closer review of one topic.
Use AP-style practice after you review the notes so you can check what you understand.
Practice free-response reasoning and compare your answer with scoring guidance.
Watch past review streams filtered to Unit 6 when you want a video walkthrough.
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get printablesAP 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.
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.
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 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.
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. 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.
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.