United States · College BoardSyllabus
Physics syllabus, dot point by dot point
Every dot point in the United States Physicssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Unit 1: Kinematics
Module overview →- How are position, velocity and acceleration defined as rates of change, and how do we calculate them for motion with constant acceleration?Topic 1.2 Displacement, Velocity, and Acceleration: define displacement, velocity and acceleration as rates of change, and apply the kinematic equations to one-dimensional motion with constant acceleration.10 min answer →
- Why does the velocity of an object depend on who is observing it, and how do we convert a velocity from one frame of reference to another?Topic 1.4 Reference Frames and Relative Motion: explain how measured position and velocity depend on the observer's reference frame, and combine velocities for relative motion along one dimension.9 min answer →
- How can the same motion be described by words, equations and graphs, and what do the slopes and areas of motion graphs tell us?Topic 1.3 Representing Motion: translate between verbal, mathematical and graphical representations of motion, and interpret the slopes and areas of position-time, velocity-time and acceleration-time graphs.10 min answer →
- How do we distinguish quantities that have only size from quantities that also have direction, and why does the difference matter for describing motion?Topic 1.1 Scalars and Vectors in One Dimension: distinguish scalar and vector quantities, and add and subtract vectors along a single dimension using a chosen sign convention.9 min answer →
- How do we resolve a vector into components, and how does treating the horizontal and vertical motions independently let us analyze projectile motion?Topic 1.5 Vectors and Motion in Two Dimensions: resolve vectors into perpendicular components, and analyze two-dimensional motion, including projectiles, by treating the horizontal and vertical motions independently.11 min answer →
Unit 2: Force and Translational Dynamics
Module overview →- Why does an object moving in a circle at constant speed still accelerate, and what provides the force that keeps it on its circular path?Topic 2.9 Circular Motion: analyze uniform circular motion using centripetal acceleration and the net inward (centripetal) force that produces it.10 min answer →
- How do we represent all the forces acting on an object and combine them to find the single net force that determines its motion?Topic 2.2 Forces and Free-Body Diagrams: identify the forces acting on an object, represent them on a free-body diagram, and calculate the net force as the vector sum of all forces.10 min answer →
- What determines the gravitational force between two masses, and how does this relate to weight and the gravitational field near a planet?Topic 2.6 Gravitational Force: use Newton's law of universal gravitation to find the force between masses, and relate this to weight and the gravitational field strength near a planet's surface.10 min answer →
- How do static and kinetic friction differ, and how do we calculate the friction force using the normal force and the coefficient of friction?Topic 2.7 Kinetic and Static Friction: distinguish static from kinetic friction, and calculate friction forces using the coefficient of friction and the normal force.10 min answer →
- Why does an object keep doing what it is doing unless a net force acts, and what does this tell us about inertia and equilibrium?Topic 2.4 Newton's First Law: state Newton's first law, relate it to inertia, and apply the condition of zero net force to objects in translational equilibrium.9 min answer →
- How does the net force on an object determine its acceleration, and how does mass mediate that relationship?Topic 2.5 Newton's Second Law: relate the net force on an object to its acceleration and mass through Fnet = ma, and use it to solve for forces, masses or accelerations.10 min answer →
- Why does every force come in a pair, and why do these paired forces not cancel each other out?Topic 2.3 Newton's Third Law: state Newton's third law, identify action-reaction force pairs, and explain why the paired forces act on different objects and so do not cancel.9 min answer →
- How does the force from a stretched or compressed spring depend on how far it is displaced, and what does Hooke's law tell us?Topic 2.8 Spring Forces: apply Hooke's law to relate the force from an ideal spring to its displacement, and use it in equilibrium and dynamics problems.9 min answer →
- What is a system, and how does treating an object or group of objects as a single point at its center of mass simplify the analysis of motion?Topic 2.1 Systems and Center of Mass: define a system and its center of mass, and explain how the center of mass of a system moves in response to external forces.9 min answer →
Unit 3: Work, Energy, and Power
Module overview →- How is the total energy of a system conserved as it changes form, and how does that let us solve problems without tracking forces over time?Topic 3.4 Conservation of Energy: apply conservation of mechanical energy to systems with conservative forces, and account for energy dissipated by nonconservative forces such as friction.11 min answer →
- How can energy be stored in the configuration of a system, and how is gravitational and elastic potential energy calculated?Topic 3.3 Potential Energy: define potential energy as stored energy of a system's configuration, and calculate gravitational potential energy (mgh) and elastic potential energy (1/2 kx^2).10 min answer →
- How fast is energy transferred or work done, and how is that rate calculated?Topic 3.5 Power: define power as the rate of energy transfer through P = W/t = Delta E/Delta t, and use P = Fv to relate power to force and speed.9 min answer →
- What is the energy an object has because it is moving, and how does it depend on the object's mass and speed?Topic 3.1 Translational Kinetic Energy: define the kinetic energy of a moving object through K = 1/2 mv^2, and reason about how it changes with mass and speed.9 min answer →
- How does a force transfer energy to or from an object as it moves, and how is that energy transfer calculated?Topic 3.2 Work: calculate the work done by a force through W = Fd cos(theta), connect net work to the change in kinetic energy, and read work as the area under a force-displacement graph.10 min answer →
Unit 4: Linear Momentum
Module overview →- How does a force acting over a time interval change an object's momentum, and what is impulse?Topic 4.2 Change in Momentum and Impulse: relate impulse to the change in momentum through J = F*t = Delta p, and read impulse as the area under a force-time graph.10 min answer →
- How do elastic and inelastic collisions differ, and which quantities are conserved in each?Topic 4.4 Collisions: analyze elastic and inelastic collisions using conservation of momentum, and distinguish them by whether kinetic energy is conserved.11 min answer →
- Why is the total momentum of a system constant when no net external force acts, and how is that principle used to solve problems?Topic 4.3 Conservation of Linear Momentum: apply conservation of momentum to an isolated system, where the total momentum before equals the total momentum after an interaction.11 min answer →
- What is linear momentum, how does it combine an object's mass and velocity, and how does it differ from kinetic energy?Topic 4.1 Linear Momentum: define linear momentum as the vector product of mass and velocity, p = mv, and distinguish it from kinetic energy.9 min answer →
Unit 5: Torque and Rotational Dynamics
Module overview →- How are the linear motion of a point on a rotating object and the angular motion of the object related?Topic 5.2 Connecting Linear and Rotational Motion: relate linear and angular quantities for a point on a rotating rigid body through v = r*omega and a = r*alpha.9 min answer →
- How does the net torque on a rigid body determine its angular acceleration, and how does rotational inertia mediate that relationship?Topic 5.6 Newton's Second Law in Rotational Form: relate the net torque on a rigid body to its angular acceleration and rotational inertia through tau_net = I*alpha.10 min answer →
- What does it mean for an object to be in rotational equilibrium, and how is Newton's first law extended to rotation?Topic 5.5 Rotational Equilibrium and Newton's First Law in Rotational Form: apply the condition of zero net torque for rotational equilibrium, alongside zero net force, to analyze balanced rigid bodies.11 min answer →
- What determines how hard it is to change an object's rotation, and how does the distribution of mass affect rotational inertia?Topic 5.4 Rotational Inertia: define rotational inertia as an object's resistance to angular acceleration, and reason about how mass and its distribution from the axis determine it.10 min answer →
- How do we describe rotational motion using angular position, velocity and acceleration, and how do the rotational kinematic equations work?Topic 5.1 Rotational Kinematics: describe rotational motion using angular displacement, angular velocity and angular acceleration, and apply the rotational kinematic equations for constant angular acceleration.10 min answer →
- What is torque, how does it depend on force and lever arm, and why does it cause rotation?Topic 5.3 Torque: calculate the torque produced by a force as tau = rF sin(theta), and identify the lever arm and the sense of rotation.10 min answer →
Unit 6: Energy and Momentum of Rotating Systems
Module overview →- What is the rotational analogue of linear momentum, and how does an angular impulse change it?Topic 6.3 Angular Momentum and Angular Impulse: define angular momentum and relate the angular impulse from a torque to the change in angular momentum.11 min answer →
- When is the angular momentum of a system conserved, and how does that explain a spinning skater speeding up?Topic 6.4 Conservation of Angular Momentum: apply conservation of angular momentum to systems with no net external torque, including changes in rotational inertia.11 min answer →
- What keeps a satellite in orbit, and how do energy and angular momentum behave in circular and elliptical orbits?Topic 6.6 Motion of Orbiting Satellites: analyze circular and elliptical orbits using gravity as the centripetal force, gravitational potential energy, and conservation of energy and angular momentum.11 min answer →
- What is the condition for rolling without slipping, and how do energy methods predict which object reaches the bottom of a ramp first?Topic 6.5 Rolling: analyze objects that roll without slipping using the v = R omega condition and the partition of energy between translation and rotation.11 min answer →
- How does a rotating object store kinetic energy, and how does that energy depend on its rotational inertia and angular velocity?Topic 6.1 Rotational Kinetic Energy: define the kinetic energy of a rotating rigid body and relate it to rotational inertia and angular velocity.10 min answer →
- How does a torque do work on a rotating object, and how is that work related to the change in its rotational kinetic energy?Topic 6.2 Torque and Work: calculate the work done by a torque through an angular displacement and apply the work-energy theorem to rotation.10 min answer →
Unit 7: Oscillations
Module overview →- What condition on the restoring force makes a system oscillate in simple harmonic motion?Topic 7.1 Defining Simple Harmonic Motion: identify simple harmonic motion by the linear restoring force F = -kx and describe the resulting oscillation.10 min answer →
- How does energy move between kinetic and potential forms in an oscillator, and how does the total energy depend on amplitude?Topic 7.4 Energy of Simple Harmonic Oscillators: analyze the interchange of kinetic and elastic potential energy in an oscillator and relate the total energy to the amplitude.11 min answer →
- What determines the period of a mass-spring system and a simple pendulum, and why is it independent of amplitude?Topic 7.2 Frequency and Period of SHM: relate frequency and period, and calculate the period of a mass-spring system and a simple pendulum.11 min answer →
- How do the position, velocity and acceleration of an SHM oscillator vary with time, and how are their graphs related?Topic 7.3 Representing and Analyzing SHM: describe the position, velocity and acceleration of an oscillator using sinusoidal functions and graphs.11 min answer →
Unit 8: Fluids
Module overview →- How do conservation of mass and energy govern a flowing fluid, and why does a fluid speed up where a pipe narrows?Topic 8.4 Fluids and Conservation Laws: apply the continuity equation and Bernoulli's equation to ideal fluid flow.11 min answer →
- What is the buoyant force on a submerged object, and how do Newton's laws decide whether it floats or sinks?Topic 8.3 Fluids and Newton's Laws: apply Newton's laws and Archimedes' principle to objects in fluids, including the buoyant force and floating versus sinking.11 min answer →
- What is a fluid, and how does density describe how its mass is distributed?Topic 8.1 Internal Structure and Density: define a fluid and describe density as mass per unit volume, an intensive property of a substance.10 min answer →
- How does a fluid exert pressure, and why does pressure increase with depth?Topic 8.2 Pressure: define pressure as force per unit area and apply the relation between pressure and depth in a static fluid.11 min answer →