AP exam review verified for 2027

AP Physics 1 Unit 6 Review: Energy & Momentum

Q: 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 .

Q: 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.

Q: 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 .

Q: 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 .

Q: 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 . 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.

Q: 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 .

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.

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AP exam review verified for 2027

What is AP Physics 1 unit 6?

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 energy and work

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 and impulse

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.

Conservation laws in rotation and orbits

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.

Conservation laws govern rotating systems

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.

AP Physics 1 unit 6 topics

6.1

Rotational Kinetic Energy

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.

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6.2

Torque and Work

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.

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6.3

Angular Momentum and Angular Impulse

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.

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6.4

Conservation of Angular Momentum

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.

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6.5

Rolling

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.

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6.6

Motion of Orbiting Satellites

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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practice snapshot

Hardest AP Physics 1 unit 6 topics

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.

4.8kMCQ attempts

Practice activity included in this snapshot.

56%average FRQ score

Across 13 scored free-response attempts for this unit.

Hardest topics in unit 6

MCQ miss rate

6.6

Motion of Orbiting Satellites

Review Motion of Orbiting Satellites with attention to how the concept appears in AP-style source and evidence questions.

53%762 tries

6.3

Angular Momentum and Angular Impulse

Review Angular Momentum and Angular Impulse with attention to how the concept appears in AP-style source and evidence questions.

49%885 tries

6.1

Rotational Kinetic Energy

Review Rotational Kinetic Energy with attention to how the concept appears in AP-style source and evidence questions.

47%884 tries

6.2

Torque and Work

Review Torque and Work with attention to how the concept appears in AP-style source and evidence questions.

39%691 tries

Unit 6 review notes

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.

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)

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.

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

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.

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

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.

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

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.

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

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.

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)

Practice AP Physics 1 unit 6 questions

Try stimulus-based AP practice questions and written prompts after you review the notes.

Example stimulus-based MCQs

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setup_diagram

Stimulus-based practice question

A block of mass $m$ hangs from a string wrapped around a massive pulley of radius $R$ , as shown in the figure. Released from rest, the block falls a distance $h$ . A student claims the work done by the string's torque on the pulley equals $mgh$ .

answer in practice

Question

Which choice best evaluates the student's claim?

The claim is correct because the string tension equals the block's weight, $mg$ .

The claim is correct because all lost gravitational potential energy goes to the pulley.

The claim is incorrect because $T<mg$ , so the pulley does less than $mgh$ of work.

The claim is incorrect because pulley work depends on fall distance, not inertia.

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Stimulus-based practice question

A grinding wheel of rotational inertia $2.0 \text{ kg}\cdot\text{m}^2$ is initially at rest. A motor applies a net torque to the wheel, as shown in the graph of torque $\tau$ versus time $t$ .

answer in practice

Question

Which of the following is most nearly the angular speed of the wheel at $t = 4.0 \text{ s}$ ?

$5.0 \text{ rad/s}$

$10 \text{ rad/s}$

$20 \text{ rad/s}$

$40 \text{ rad/s}$

Example FRQs

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FRQ

Rotational inertia determination through torque and angular acceleration

3. Students are investigating how a constant torque applied for a measured time interval changes the angular speed and rotational kinetic energy of a rigid system.

Describe an experimental procedure to collect data that would allow the students to determine the rotational inertia $I$ of the disk. Include any steps necessary to reduce experimental uncertainty.

Describe how the data collected in part A could be graphed and how that graph would be analyzed to determine $I$ .

Figure 1. Disk-on-axle torque apparatus with hanging mass and photogate measurement of angular speed.

Time of pull, t (s)	Angular speed after pull, c9 (rad/s)
0.40	8.2
0.60	12.0
0.80	15.9
1.00	20.4
1.20	24.1

The students use the setup shown in Figure 1 with a hanging mass of $m = 0.200\ \text{kg}$ . The radius of the small axle is $r = 0.0200\ \text{m}$ . The disk starts from rest each trial. The students allow the mass to fall for a measured time interval $t$ and then stop the string from unwinding so no additional torque is applied. Immediately after the pull, the students measure the disk’s angular speed $\omega$ using the photogate. The measured values of $t$ and $\omega$ are shown in Table 1.

Assume the torque on the disk during the pull is constant and is given by $\tau = m g r$ , where $g = 9.80\ \text{m/s}^2$ .

The students correctly determine that the relationship between $\omega$ and $t$ is $\omega = (\tau/I)t$ .

The students create a graph with $t$ plotted on the horizontal axis.

Indicate what measured or calculated quantity could be plotted on the vertical axis to yield a linear graph whose slope can be used to calculate an experimental value for the rotational inertia $I$ of the disk.

Vertical axis: Horizontal axis: $t$

ii.

On the blank grid provided, create a graph of the quantities indicated in part C(i) that can be used to determine $I$ .

•

Use Table 2 to record the data points or calculated quantities that you will plot.

•

Clearly label the vertical axis, including units as appropriate.

•

Plot the points you recorded in Table 2.

iii.

Draw a straight best-fit line for the data graphed in part C(ii).

Using the best-fit line that you drew in part C(iii), calculate an experimental value for the rotational inertia $I$ of the disk. A student uses two points on the best-fit line from part C(iii): $\left(t_1 = 0.40\ \text{s},\ \omega_1 = 8.0\ \text{rad/s}\right)$ and $\left(t_2 = 1.20\ \text{s},\ \omega_2 = 24.0\ \text{rad/s}\right)$ . The student assumes $\tau = mgr$ with $m = 0.200\ \text{kg}$ , $g = 9.80\ \text{m/s}^2$ , and $r = 0.0200\ \text{m}$ .

Figure 2. Modified setup with an additional identical disk mounted coaxially to form a rigid two-disk system, using the same constant-torque hanging-mass drive.

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FRQ

Rotating disk-ring system angular momentum behavior

1. A rigid system consists of a uniform solid disk and a thin ring that are rigidly attached and rotate together about a vertical, frictionless axle through their common center, as shown in Figure 1.

Figure 1. Top view of a rigid disk–ring system rotating about a vertical, frictionless axle; a tangential force F is applied at the ring’s outer rim. Counterclockwise is defined as the positive rotation direction.

Figure 2. Axes for plotting net torque τ_net versus time t from t = 0 to t = t₁.

On the axes shown in Figure 2, sketch a graph of the net torque $\tau_{\text{net}}$ exerted on the disk-ring system as a function of time $t$ from $t=0$ to $t=t_1$ .

ii.

Derive an expression for the magnitude of the angular impulse $J_\tau$ delivered to the disk-ring system from $t=0$ to $t=t_1$ in terms of $F$ , $R$ , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

iii.

Derive an expression for the rotational work $W_{\text{rot}}$ done on the disk-ring system by the applied force from $t=0$ to $t=t_1$ in terms of $F$ , $R$ , and $\theta_1$ . Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Indicate whether the magnitude of the angular momentum of the disk-ring system about the axle increases, decreases, or remains constant during $0 < t < t_1$ . The student now considers angular momentum for the disk-ring system about the axle during the interval $0 < t < t_1$ .

Increases
Decreases
Remains constant
Justify your response.

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FRQ

Rotating disk with falling block energy conversion

2. A light string is wrapped around the rim of a uniform solid disk that can rotate about a fixed, frictionless axle, as shown in Figure 1.

Figure 1. A block of mass m = 0.300 kg hangs from a light string wrapped around the rim of a uniform solid disk (radius R = 0.200 m) on a fixed frictionless axle. Three snapshots show the block at y = 0 (release), y = 0.300 m, and y = 0.600 m below the release point. The downward displacement y is measured vertically downward from the release level.

Figure 2. Energy bar chart at release (block at y = 0). Bars represent K_trans of the block, K_rot of the disk, and gravitational potential energy Ug of the system, with Ug defined to be zero at y = 0.600 m.

Figure 3. Energy bar chart when the block has fallen to y = 0.300 m (halfway to the bottom). Ug is defined to be zero at y = 0.600 m; total mechanical energy matches Figures 2 and 4.

Figure 4. Reference energy bar chart at the bottom position y = 0.600 m where U_g is defined to be zero. The remaining mechanical energy is split into translational kinetic energy of the block and rotational kinetic energy of the disk.

Draw shaded bars that represent $K_{\text{trans}}$ , $K_{\text{rot}}$ , and $U_g$ to complete the energy bar charts in Figure 2 and Figure 3 for when the block is released from rest at $y=0$ and for when the block is at $y=0.300\ \text{m}$ , respectively. Figure 4 shows an energy bar chart that represents the translational kinetic energy $K_{\text{trans}}$ of the block, the rotational kinetic energy $K_{\text{rot}}$ of the disk, and the gravitational potential energy $U_g$ of the block-disk-Earth system at the instant the block is at $y=0.600\ \text{m}$ . The gravitational potential energy $U_g$ of the system is defined to be zero at $y=0.600\ \text{m}$ .

• Shaded bars should start at the dashed line that represents zero energy.
• Represent any energy that is equal to zero with a distinct line on the zero-energy line.
• The relative heights of each shaded bar should reflect the magnitude of the respective energy consistent with the scale used in Figure 4.

Figure 5. Initial and final states for the falling block and rotating disk. The string unwraps without slipping, so the block’s speed v equals Rω.

Starting with conservation of energy, derive an equation for the angular speed $\omega$ of the disk when the block has fallen $0.600\ \text{m}$ . Express your answer in terms of $m$ , $g$ , $y$ , $I$ , and $R$ . Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Figure 5 shows the system when the block is released from rest at $y=0$ and at the instant the block reaches $y=0.600\ \text{m}$ . The string does not slip, so $v = R\omega$ . Assume the axle is frictionless and the string is light.

Figure 6. Angular momentum of the disk about the axle versus time. The provided straight line indicates L increases linearly from t = 0 to t = 0.60 s; students add angular impulse and work representations.

The torque exerted by the string on the disk about the axle is constant in time while the block is falling, and the disk starts from rest. Figure 6 shows a graph of the angular momentum $L$ of the disk about the axle as a function of time from $t=0$ to $t=0.60\ \text{s}$ .

Sketch and label on Figure 6 a representation of the angular impulse delivered to the disk from $t=0$ to $t=0.60\ \text{s}$ that is consistent with the straight-line graph provided.

ii.

Sketch and label on Figure 6 a representation (in terms of area or another clear graphical feature) that corresponds to the work done by the torque on the disk from $t=0$ to $t=0.60\ \text{s}$ . Your sketch must be consistent with the straight-line $L(t)$ graph and with the relationship between work and rotational kinetic energy.

Indicate whether the angular momentum of System 2 about the axle is conserved from release until $t=0.60\ \text{s}$ . A student claims that because the disk's angular momentum increases during the fall, angular momentum is conserved for the system. Consider two different choices of system: System 1 is the disk alone, and System 2 is the disk + block. Neglect the rotational inertia of the string.

Conserved
Not conserved
Justify how your response is consistent with the system choice and with the representations in part C.

write this FRQ

Key terms

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.

Common unit 6 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.

How this unit shows up on the AP exam

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 unit 6 review checklist

Calculate rotational kinetic energyApply 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 torqueUse 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 waysUse 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 theoremRelate 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 momentumIdentify 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 motionApply 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 orbitsDistinguish 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.

How to study unit 6

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.

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Topic study guides

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Watch past review streams filtered to Unit 6 when you want a video walkthrough.

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Cheatsheets

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Frequently Asked Questions

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.

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.

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.

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. 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.

Ready to review Unit 6?Start with the notes, check the topic cards, and use the practice or resource links when they are available for this course.

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