Curriculum
Physics
48 entries across 5 tiers. Each tier builds on the tiers before it, so read top to bottom and every idea arrives after its prerequisites. Where an entry has entries to read first, they are listed under it.
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T0 Primitives and observation
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- Dimensional analysis in physics
Dimensional reasoning · Reject or repair a formula before collecting data.
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- Units, standards, and calibration Checking that both sides of an equation carry the same dimensions presupposes an agreed system of base units in which those dimensions are expressed.
- Observation, measurement, and physical quantities
Foundations of measurement · Design a measurement procedure another person can reproduce.
- Precision, accuracy, and uncertainty
Measurement and error · Report a measurement honestly instead of hiding error behind digits.
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- Observation, measurement, and physical quantities You cannot ask how good a measurement is until you have first pinned down what measuring that quantity even means.
- Units, standards, and calibration You can only ask how close a reading is to the true value once the true value is defined against an agreed standard.
- Physical models and idealization
Modeling and idealization · State what a model ignores and predict where it will fail.
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- Precision, accuracy, and uncertainty Knowing how much uncertainty a measurement already carries is what lets you judge whether a model's simplifications are still within the noise or are the actual source of a mismatch.
- Reference frames and relative description
Reference frames · Translate a motion description between moving observers.
- Units, standards, and calibration
Standards and calibration · Calibrate a simple measuring device and state its uncertainty.
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- Observation, measurement, and physical quantities Once a quantity is defined by a repeatable procedure, that procedure needs a shared, fixed standard before two different people's numbers can mean the same thing.
T1 Core relationships and structures
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- Action-reaction pairs
Dynamics and forces · Explain propulsion without invoking something to push against.
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- Force as interaction Defining force as something that always involves two bodies is what makes the pairing of forces on those two bodies almost automatic.
- Force as interaction
Dynamics and forces · Draw a complete interaction map for a physical system.
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- Inertia and the persistence of motion Naming force as whatever changes an object's motion away from its inertial state requires first establishing that unforced motion persists rather than needing continuous cause.
- Mass as resistance to acceleration
Dynamics and forces · Compare masses through controlled acceleration.
- The relation between force, mass, and acceleration
Dynamics and forces · Predict motion from a net force and test the prediction.
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- Force as interaction You need a clean, interaction-based notion of force before you can ask how much acceleration a given force produces in a given object.
- Mass as resistance to acceleration Mass is the proportionality constant that links force and acceleration, so it must be defined before that relation can be derived rather than merely stated.
- Universal gravitation
Dynamics and forces · Estimate gravitational force and identify when simpler approximations work.
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- Circular motion and inward acceleration Deriving that gravity supplies the inward acceleration of an orbit requires the centripetal acceleration formula first.
- Weight and gravitational interaction Weight is the local, near-Earth special case that the general inverse-square law of gravitation must reduce to at the planet's surface.
- Weight and gravitational interaction
Dynamics and forces · Predict how a scale reading changes in elevators or other accelerations.
- Conservation of mechanical energy
Energy and work · Predict speed or height without solving every moment of motion.
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- Kinetic energy Mechanical energy conservation is the claim that kinetic energy plus potential energy stays constant, which requires kinetic energy to be defined first.
- Potential energy and configuration You cannot track the exchange between motion and configuration until configuration itself has a quantity attached to it.
- Kinetic energy
Energy and work · Compare crash severity or braking needs at different speeds.
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- Work as force through distance Kinetic energy is defined as the work required to accelerate a mass from rest to a given speed, so work must be defined first.
- Potential energy and configuration
Energy and work · Choose a reference and compute gravitational or elastic changes.
- Work as force through distance
Energy and work · Distinguish effort from mechanical energy transfer.
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- Dot product as alignment Work done by a force through a displacement is defined as the dot product of the force and displacement vectors.
- The relation between force, mass, and acceleration Computing work as force applied over a distance presupposes a precise, quantitative meaning of force, which this relation supplies.
- Kinetic friction and energy loss
Forces and contact mechanics · Predict stopping distance and thermal loss.
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- Static friction Once the required force exceeds the static maximum, the same contact begins to slide and the kinetic friction regime takes over.
- Work as force through distance Energy lost to friction is calculated as negative work done by the friction force over the sliding distance.
- Normal force and contact constraints
Forces and contact mechanics · Solve contact problems without assuming normal force always equals weight.
- Static friction
Forces and contact mechanics · Find whether an object will remain stuck before calculating motion.
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- Normal force and contact constraints The maximum available static friction is set as a fraction of the normal force, so sticking cannot be analyzed without first solving for the normal force.
- Tension in strings and cables
Forces and contact mechanics · Analyze pulleys or suspended loads with clear force diagrams.
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- Normal force and contact constraints Both are contact constraint forces solved the same way, as whatever value keeps a rigid or inextensible connection from being violated.
- Acceleration
Kinematics · Infer forces or motion from a velocity-time pattern.
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- Speed and velocity Acceleration is defined as the rate of change of velocity, so velocity must be a settled, directed quantity before a rate of change of it means anything.
- Inertia and the persistence of motion
Kinematics · Identify hidden friction in everyday claims that motion needs force.
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- Physical models and idealization Inertia is only visible once friction and air resistance are idealized away, so grasping idealization is what makes the frictionless case worth imagining at all.
- Motion graphs
Kinematics · Reconstruct one motion graph from another.
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- Acceleration Reading acceleration as the slope of a velocity time graph, and displacement as area under it, requires the definition of acceleration to already be in hand.
- Speed and velocity Reading a velocity value off the slope of a position time graph requires already knowing that velocity is a rate, not a raw distance covered.
- Position, distance, and displacement
Kinematics · Represent a route numerically and geometrically.
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- Reference frames and relative description Position and displacement are only meaningful once a reference frame fixes the point and axes they are measured against.
- Speed and velocity
Kinematics · Explain how equal speeds can produce different motions.
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- Position, distance, and displacement Velocity is defined as the rate of change of position, so displacement must already be pinned down as a directed change before a rate of change can mean anything.
- Reference frames and relative description A velocity value is always a velocity relative to some frame, so describing motion at all requires first choosing and stating that frame.
- Two-dimensional motion and projectiles
Kinematics · Predict a projectile path and test it experimentally.
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- Acceleration Projectile motion is built from a constant downward acceleration acting alongside an unaccelerated horizontal velocity, so the concept of acceleration must precede combining the two.
- Motion graphs Predicting a projectile path by combining independent horizontal and vertical motions is easiest to check by reasoning about each motion's own position and velocity time graph first.
- Position, distance, and displacement Decomposing a curved path into independent horizontal and vertical parts requires treating displacement as a vector with components in the first place.
- Vectors as directed quantities Position, velocity, and acceleration in more than one dimension are vector quantities, and projectile motion is the standard first place they are combined.
- Elastic and inelastic collisions
Momentum and collisions · Predict post-collision motion and energy loss.
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- Impulse and force over time The impulse each body exerts on the other during contact is what changes their individual momenta in a collision.
- Kinetic energy Collisions are classified by how much kinetic energy survives the impact, so comparing kinetic energy before and after is the basic diagnostic tool.
- Momentum as quantity of motion Every collision analysis starts from the conserved total momentum of the colliding bodies.
- Impulse and force over time
Momentum and collisions · Explain airbags, padding, and follow-through quantitatively.
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- Momentum as quantity of motion Impulse is defined as the change in momentum a force produces, so momentum must be defined first.
- Momentum as quantity of motion
Momentum and collisions · Analyze recoil and collisions using system boundaries.
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- Action-reaction pairs Conservation of momentum in collisions and recoil follows directly from every interaction producing equal and opposite forces on the two bodies involved.
- The relation between force, mass, and acceleration Momentum's rate of change under a force is derived from this exact relation, extended to allow mass itself to change.
- Circular motion and inward acceleration
Rotational and orbital motion · Calculate turning requirements for a vehicle or orbit.
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- Angles, rotation, and radians Angular speed and linear speed around a circular path are related through the radian definition of angle established here.
- Circles, radius, and pi Describing motion around a circular path requires the radius and circumference relationships established here to connect rotational and linear quantities.
- Two-dimensional motion and projectiles Circular motion is understood by the same trick of splitting motion into components under a known acceleration, here applied to a constantly redirected rather than constantly downward acceleration.
- Angular momentum
Rotational mechanics · Predict spin changes when mass moves inward or outward.
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- Circular motion and inward acceleration Rotational quantities build on the same radius-and-rotation-rate description of circular motion developed here.
- Cross product as oriented area and rotation Angular momentum is defined as the cross product of a position vector and a momentum vector, extending the same construction from force to motion.
- Rotational inertia Angular momentum is defined using rotational inertia multiplied by angular velocity, so rotational inertia must exist first.
- Center of mass and balance
Rotational mechanics · Design a stable object or diagnose why it tips.
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- Rotational inertia How mass is distributed around a pivot, the same fact that sets rotational inertia, also determines where a body's effective balance point sits.
- Rotational inertia
Rotational mechanics · Compare wheel or flywheel designs without relying only on total mass.
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- Torque and rotational effect Rotational inertia is defined as the constant relating torque to angular acceleration, so torque must be established first.
- Static equilibrium
Rotational mechanics · Solve a bridge, ladder, or balanced-beam problem.
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- Angular momentum A body with zero net torque and no changing angular momentum is the rotational half of the equilibrium condition.
- Center of mass and balance Whether a supported body stays at rest depends on whether the center of mass sits over the base of support, making it a direct input to equilibrium reasoning.
- Tension in strings and cables Suspended loads and cable systems are among the standard worked cases of bodies held motionless by balanced forces, including tension.
- Torque and rotational effect True rest requires zero net torque as well as zero net force, so equilibrium reasoning depends on torque being defined.
- Torque and rotational effect
Rotational mechanics · Choose where and how to apply force to rotate an object efficiently.
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- Cross product as oriented area and rotation Torque is defined as the cross product of the position vector from a pivot and the applied force.
T2 Mechanisms and transformations
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- Conduction, convection, and radiation
Thermodynamics · Choose insulation or cooling strategies for a design.
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- The second law and irreversibility All three heat transfer mechanisms move energy spontaneously from hot to cold and never reverse on their own, which is the second law playing out in a concrete setting.
- Heat as energy transfer
Thermodynamics · Track heat separately from internal energy and temperature.
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- Temperature as microscopic energy distribution Heat is defined as energy that flows because two systems have different temperatures, so temperature must be defined first.
- Internal energy
Thermodynamics · Write an energy account for heating, compression, or phase change.
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- Heat as energy transfer To write a correct energy account for a system you must first be able to separate heat, energy crossing a boundary, from the energy already stored inside.
- Phase transitions
Thermodynamics · Read or construct a phase-change energy curve.
- Pressure from microscopic collisions
Thermodynamics · Predict how pressure changes with depth, temperature, or confinement.
- Temperature as microscopic energy distribution
Thermodynamics · Explain thermal equilibrium from particle exchange.
- The first law of thermodynamics
Thermodynamics · Build a complete energy balance for a piston or thermal system.
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- Heat as energy transfer The first law is a bookkeeping statement about heat and work, so heat must first be defined as a process quantity rather than a stored one.
- Internal energy The first law states how internal energy changes in terms of heat and work, so internal energy must first be defined as the thing being tracked.
- The ideal gas model
Thermodynamics · Predict gas behavior and state when the model breaks.
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- Dimensional analysis in physics Confirming that a proposed relation among pressure, volume, and temperature is dimensionally consistent is the first filter a physical model must pass before its predictions are trusted.
- Physical models and idealization Treating gas molecules as point particles with no volume and no attraction between them is an explicit idealization whose stated scope this entry teaches how to evaluate.
- Pressure from microscopic collisions This derivation of pressure from molecular collisions is the exact mechanism combined with temperature to produce the ideal gas law.
- Temperature as microscopic energy distribution The ideal gas law ties pressure, volume, and temperature together, and that link only makes sense once temperature is understood as molecular kinetic energy.
- The second law and irreversibility
Thermodynamics · Identify the cost paid by any engine, refrigerator, or computation.
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- Kinetic friction and energy loss Friction converting organized kinetic energy into disorganized heat is the clearest mechanical example of the one-way arrow the second law generalizes.
- The first law of thermodynamics The first law establishes that energy is conserved in every process; the second law then adds the further constraint on which conserving processes can actually occur.
T3 Systems and interaction
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- Damping, driving, and resonance
Oscillations and waves · Avoid a destructive resonance or exploit one on purpose.
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- Oscillation and restoring forces Resonance is what happens when a periodic push meets a system's own restoring behavior, so the undamped oscillator's natural frequency has to exist as a concept before energy loss and driving can be layered onto it.
- Oscillation and restoring forces
Oscillations and waves · Build and tune a spring or pendulum oscillator.
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- Conservation of mechanical energy The back-and-forth exchange between kinetic and potential energy is the energy account of every oscillator.
- Second-order dynamics The spring and pendulum equations derived here are the mathematical skeleton underneath the physical account of restoring forces and oscillation.
- Springs, dampers, and suspension The spring's linear restoring force introduced here is the mechanism a later treatment of oscillation generalizes into periodic motion.
- Waves as travelling disturbances
Oscillations and waves · Predict how wave speed, wavelength, and frequency constrain one another.
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- Oscillation and restoring forces A travelling wave is a chain of oscillators handing motion to their neighbors, so the behavior of one oscillator in isolation is the unit a wave is assembled from.
T5 Advanced synthesis and limits
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- Orbit as continuous free fall
Rotational and orbital motion · Predict how speed and altitude shape an orbit.
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- Angular momentum Orbital motion under a central force conserves angular momentum, which is why orbiting bodies speed up near closest approach and slow down far away.
- Universal gravitation Orbital motion is the case of continuous free fall under exactly the inverse-square gravitational force this entry derives.