Physics Approximations

The physicist’s favourite trick

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Binomial approximation: $(1 + x)^n \approx 1 + nx$ for small $x$.
• Keeping the first terms gives famous formulas: mgh, ½mv², simple harmonic motion.
• Series also evaluate 0/0 limits by comparing leading terms.

Steps

1. A square root without a calculator
2. Keep the first terms
3. Where g comes from
4. Big swings
5. Why linearise?
6. A limit by series