Math, Physics & Models

Learn the Tools of the Trade

Why Tools Matter

Engineers use mathematics and physics to build simplified models of the real world. These models let us:

Why Math & Physics?

Math is the language of patterns, and physics describes how the universe behaves. Together they give engineers a foundation for building models that are simple but useful.

Key Tool: Dimensional Analysis

This is a way to check whether equations make sense — by comparing units. For example, if you calculate a force using speed and distance, something’s probably wrong!

Key Tool: Free‑Body Diagrams

These diagrams show all the forces acting on an object. They help engineers visualize interactions before writing equations or building prototypes.

A Simple Example

If you push a cart with twice the force, it accelerates twice as much (in ideal conditions). This is a model based on Newton’s Second Law: Force = Mass × Acceleration.

Try It

Imagine you’re choosing between two wheels for a design: one heavy and one light. Which would you pick for speed? For strength? What tradeoffs are you considering?

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