Dimensional Analysis

Intro

Dimensional analysis is the process of checking and reasoning about the units of physical quantities. It ensures formulas make sense, helps prevent errors, and helps converting between units.

Basic Principles

1. Every physical quantity has a dimension (length [L], time [T], mass [M], etc.)
2. Units in an equation must match on both sides
3. Multiplying/dividing quantities combines/cancels units accordingly

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Examples

Physics / Motion

$$\text{distance}=\text{speed}\times \text{time}$$

• Units check: $[L]=[L/T]\times [T]$
• Demonstrates how distance scales with speed and elapsed time.

Conversion Factors