Keep the useful ideas close

Physics formulas, with a reason.

Every equation links to an experiment. Check the assumptions before applying it.

Motion

Projectile motion

x = v₀ cos(θ)t · y = v₀ sin(θ)t − ½gt²

Point particle launched and landing at the same height; uniform gravity and no air resistance.

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Motion

Position, velocity & acceleration

x = v₀t + ½at² · v = v₀ + at

One-dimensional motion starting at x = 0 with constant acceleration.

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Forces & energy

Force & friction

Fnet = ma · fs ≤ μsN · fk = μkN

Horizontal surface, rightward applied force, g = 9.81 m/s². For comparison, static and kinetic coefficients both equal μ. The block starts at rest.

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Forces & energy

Energy on a ramp

mgh₀ = mgh + ½mv²

A sliding point mass starts from rest. No friction, air drag, or rotational energy; g = 9.81 m/s².

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Waves

Pendulum explorer

T = 2π√(L/g)

Small-angle approximation, massless rod/string, point bob, no damping. Angles are limited to 15°.

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Waves

Spring oscillator

F = −kx · T = 2π√(m/k)

Horizontal ideal Hooke’s-law spring, no friction or damping. Displacement is measured from equilibrium.

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Waves

Traveling wave explorer

v = fλ · y = A sin(2π(x/λ − ft))

An ideal transverse sinusoidal wave. Frequency and wavelength are independently set; wave speed changes with their product.

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Electricity

Ohm’s law & power

V = IR · P = VI

Ideal DC voltage source and an ohmic resistor with constant resistance; wires have zero resistance.

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Electricity

Series & parallel resistors

Series: R = R₁ + R₂ · Parallel: 1/R = 1/R₁ + 1/R₂

Two ideal ohmic resistors, ideal DC source, zero-resistance wires.

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Optics

Refraction & total internal reflection

n₁ sin θ₁ = n₂ sin θ₂

Flat interface between transparent media. Angles are measured from the normal; ray intensity and partial reflection are not modeled.

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Optics

Converging lens explorer

1/f = 1/dₒ + 1/dᵢ · M = −dᵢ/dₒ

Ideal thin converging lens and paraxial rays. A positive object distance represents a real object; negative image distance represents a virtual image.

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Forces & energy

Buoyancy & floating

Fᵦ = ρfluid g Vsubmerged · W = ρobject g V

Uniform fluid and object. Submerged fraction is set by the control. Only gravity and buoyancy are shown; drag and any external force holding the object are excluded. g = 9.81 m/s².

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