Where is the object?
Choose a coordinate system.
A physical description begins by defining the frame and variables that locate the system.
Side 17
Physics
A study of how physical systems change, interact and conserve structure. Physics builds simplified models, derives consequences mathematically, then forces those predictions into contact with measurement.
system→model→law→prediction→measurement
06domains
05conservation ideas
05model habits
17Side
Start with change in motion.
Classical mechanics asks how position, velocity and acceleration evolve, and how forces alter that evolution.
How fast is position changing?
v = dx/dt
Velocity carries both magnitude and direction.
How fast is velocity changing?
a = dv/dt
An object can accelerate by changing speed, direction or both.
What changes the motion?
F = ma in the classical regime.
Net force determines acceleration for a body of constant mass.
What motions are actually allowed?
Surface, joint, string, orbit?
Constraints remove degrees of freedom and introduce reaction forces.
Newtonian modelnet force = rate of change of momentum
Conservation can simplify what forces make messy.
When symmetries or isolation conditions apply, quantities such as energy and momentum can remain constant even while the system changes internally.
Energy of motion.
For a classical particle, kinetic energy scales with mass and the square of speed.
Energy associated with configuration.
Gravitational, elastic and electric interactions can be represented through potential-energy functions.
Force acting through displacement.
Net work changes kinetic energy; conservative forces can trade kinetic and potential energy.
Mass × velocity.
Total momentum is conserved in an isolated system, making collisions easier to analyze.
Rotational analogue of momentum.
It is conserved when no external torque acts on the system.
Rate of energy transfer.
Two machines can perform the same work while differing in how quickly they do it.
Interactions can be represented throughout space.
A field assigns a physical quantity to each point in space and time, allowing distant interactions to be treated locally.
Gravitational field
Source
Mass-energy
In Newtonian gravity, mass generates an attractive field; general relativity later reframes gravity geometrically.
Effect
Acceleration
A test mass responds to the local gravitational field.
Potential
Energy landscape
Potential provides a scalar description related to the field through spatial change.
Electromagnetic field
Charge
Electric interaction
Electric fields act on charge and can store energy.
Current
Magnetic interaction
Moving charge and changing electric fields are associated with magnetic fields.
Coupling
Changing fields generate one another.
Maxwell’s equations unify electricity, magnetism and electromagnetic waves.
A field is not merely a drawing of arrows.
It is a mathematical object with values defined across space-time, used to predict how matter or other fields respond.
Disturbances propagate.
Wave descriptions connect local oscillation with transport through space and time.
| Quantity | Meaning | Relationship | Question |
|---|---|---|---|
| Amplitude | Maximum size of oscillation. | Often tied to energy or intensity. | How strong is the disturbance? |
| Frequency | Cycles per unit time. | f = 1/T | How rapidly does it oscillate? |
| Wavelength | Spatial period. | v = fλ | How far apart are matching phases? |
| Phase | Position within a cycle. | Controls interference. | Are oscillations aligned? |
| Group behavior | Envelope or packet motion. | Can differ from phase velocity. | How does information or energy propagate? |
Waves combine.
Superposition can produce reinforcement or cancellation depending on phase.
Driving matches a natural mode.
Small repeated forcing can create large responses near a system’s resonant frequency.
Waves spread around openings and obstacles.
The effect becomes prominent when dimensions are comparable to wavelength.
Macroscopic order emerges from microscopic multiplicity.
Thermodynamics tracks energy, heat, work and entropy without needing the exact trajectory of every microscopic particle.
State variables
Pressure, volume, temperature and composition summarize macroscopic state.
First law
Energy is conserved: changes in internal energy arise through heat and work transfers.
Entropy
Entropy tracks the number of accessible microscopic arrangements and constrains spontaneous macroscopic change.
Second law
For an isolated system, entropy does not spontaneously decrease.
Statistical mechanics
Macroscopic thermodynamic behavior is connected to probability distributions over microscopic states.
Thermal habitmicrostates → probabilities → macroscopic regularity
Classical intuition has boundaries.
Relativity and quantum mechanics revise assumptions that work extremely well at everyday scales but fail at very high speeds, strong gravity or microscopic scales.
Space and time depend on frame.
The speed of light is invariant for inertial observers; simultaneity, time intervals and lengths are frame-dependent.
Energy contributes to inertia.
Mass and energy are related within relativistic dynamics rather than being completely separate conserved substances.
Gravity becomes geometry.
Matter-energy influences spacetime geometry, while geometry shapes free-fall motion.
Some physical quantities occur in discrete structures.
Atomic and subatomic systems require quantum states rather than classical trajectories alone.
States combine linearly.
A quantum system can be represented as a combination of possible basis states before measurement.
Some observables cannot be simultaneously sharp.
Quantum uncertainty is structural to the theory, not merely poor instrumentation.
Model domains matter.
Newtonian mechanics is not “wrong” because relativity exists; it remains an excellent approximation within the regime where relativistic corrections are negligible.
University PhysicsYoung & Freedman · broad classical foundation
The Feynman Lectures on PhysicsFeynman, Leighton & Sands · conceptual depth
Six Easy PiecesRichard Feynman · core principles
Concepts of Modern PhysicsArthur Beiser · modern overview