Math Playground
All topics

Topic

Physics

Math made tangible. Drop a ball, launch a projectile, and watch the equations play out in motion.

Why physics here?

Physics is the easiest place to see why math matters. The equations describe falling, throwing, swinging — things you can already feel intuitively. The math just makes the intuition precise.

Motion

Position, velocity, acceleration — a falling ball.

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Projectile

Launch at any angle and watch the parabola play out.

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Gravity

Drop a feather and a hammer in vacuum — they land together. Why?

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Forces & Newton's laws

Push, pull, friction, equal-and-opposite — Newton's three rules in motion.

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Newton's laws of motion

Inertia, F=ma, action–reaction — the three laws all of mechanics rests on.

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Force types

Gravity, normal, friction, tension, applied — pick the force, see the effect.

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Force calculations

Add force vectors, find the net push — and use F = ma.

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Energy

Kinetic, potential and the law that says energy never disappears.

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Energy & work

W = F·d. Push something through a distance — and you've done work.

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Power

How fast energy is transferred — watts, horsepower, joules per second.

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Momentum & collisions

Mass × velocity. Watch billiard balls trade momentum on collision.

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Collisions

Elastic vs inelastic — what survives a crash, what doesn't.

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Conservation laws

Energy, momentum, charge — quantities the universe insists on keeping.

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Spring

Hooke's law: F = −kx. Push or pull — the spring pushes back proportionally.

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Pendulum

Swing time depends on length, not on weight — Galileo's discovery.

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Double pendulum

Two arms, infinite chaos — small changes spawn wildly different paths.

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Moment & torque

Force times lever arm — the rotational version of force.

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Waves & sound

Wavelength, frequency and pitch — see and hear the difference.

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Sound waves

Compressions and rarefactions in air — how your ears hear pitch and loudness.

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Radio & microwaves

Long wavelength, low energy — but they carry every podcast you stream.

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Seismic waves

P-waves, S-waves and surface waves — how earthquakes travel.

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Doppler effect

Why a siren goes high then low as it passes — wavelength compresses, then stretches.

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Beats

Two close frequencies — and a third, slow oscillation appears.

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Diffraction

Waves bend around corners and through slits — and interfere with themselves.

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Reflection (waves)

Angle in equals angle out — for light, sound or any wave.

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Refraction

Light bends as it changes medium — that's why a straw looks broken in water.

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Light

Wave, particle, both — and why your screen can show every colour.

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Lumen, lux & candela

Three ways to measure brightness — output, density and intensity.

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Electromagnetic spectrum

Radio to gamma — light is only the small bit your eyes can see.

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Infrared

Just past red — heat radiation, remote controls, night-vision.

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Ultraviolet

Just past violet — invisible to you, but a sunburn will tell you it's there.

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X-rays & gamma

The high-energy end — they cut through skin and split atoms.

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Electricity & circuits

Voltage, current, resistance — Ohm's law lit up in a tiny circuit.

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Electric charge & fields

Two charges in space. Watch the field lines push and pull.

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Electric circuits

Voltage pushes, resistance pushes back — Ohm's law ties them together.

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Electric power

P = VI. How much energy a circuit eats per second.

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Electricity-water analogy

Voltage as pressure, current as flow — make circuits intuitive.

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Magnetism

Why a magnet sticks — and why every magnet has two poles.

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Fields

Gravity, electric, magnetic — how forces reach across empty space.

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Solar system

Planets, orbits and the maths Kepler and Newton used to describe them.

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Atoms

Electrons orbit a nucleus. Build atoms shell by shell.

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Atom — electrons

Electrons live in shells — and the shells fill in a fixed order.

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Atom — orbitals

s, p, d, f — fuzzy probability clouds, not little planets.

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Periodic table

Why elements line up the way they do — electron shells, predicted.

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Entropy

Why broken glass doesn't reassemble — disorder always wins.

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Quantum mechanics

A particle that's a wave. Probability replaces certainty.

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Heisenberg uncertainty

Position and momentum — you can't pin both down at the same time.

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Quantum & polarisation

Stack three polarising filters — and more light gets through. Welcome to quantum.

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Bra-ket notation

⟨ψ| and |φ⟩ — the language quantum mechanics is written in.

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Ultraviolet catastrophe

Classical physics predicted infinite UV light from a hot box. Quanta fixed it.

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Relativity

Speed up to near light-speed and watch a clock slow down.

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Relativity (special)

Speed of light is constant — so time and space have to bend.

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Units & equations

SI units, dimensional analysis, why every equation must balance.

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