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Chapter 0 · Prep Physics — Rearranging Equations

Equation Rearranger

A Manim-style lesson film you steer: click any variable and watch it isolated step by step, typeset like a 3Blue1Brown video. The operation is written on both sides, the cancelling pieces flash red and are struck through with the reason (m/m = 1), and everything else glides into place. Play it through, pause mid-move, step back and forth, or jump to any step. 20 equations, from F = ma to Newton's law of gravitation, Coulomb's law and T = 2π√(L/g).

Newton's Second Law
Typesetting…
Click a variable in the equation to solve for it
The Golden Rule

Whatever you do to one side, you must do to the other. Watch the operation appear on both sides at once — a real new fraction or a real new term, not a floating label.

The pieces that cancel flash red and are struck through, with the reason written above (m/m = 1). Then everything else slides into the simplified equation.

The variable you are solving for is yellow throughout; every other variable keeps its own colour, and constants (G, k, π, ½, ε₀, c) are grey.

Play runs the whole derivation like a film; Next takes one step at a time. Space pauses, ← → step, F goes full screen. Click a step to jump straight to it.

Try This

1. Click a in F = ma. Both sides are divided by m; the two m’s cancel, leaving a on its own.

2. Switch to ρ = m/V and click V. V climbs out of the denominator first, then ρ is cleared the same way — two moves, in the right order.

3. When a derivation finishes, click a different variable: it carries on from what is on screen.

F = m × a

Click a variable to watch it isolate.

What Each Variable Means

F

force (N)

m

mass (kg)

a

acceleration (m/s²)