"Students frequently struggle not with the calculus itself, but with setting up the initial free-body diagrams and coordinate systems from descriptive word problems."
1. The 5-Step Translation Pipeline
1. Extract Given Quantities with SI Units.
2. Define the Reference Frame and Coordinate Axes (Assigning positive and negative directions).
3. Isolate the Governing Physical Law (e.g., Work-Energy Theorem vs Momentum Conservation).
4. Formulate the Differential or Algebraic Equation in pure KaTeX notation.
5. Check Dimensional Homogeneity before calculating numerical values.
2. Dimensional Analysis as an Instant Sanity Check
Always ask the AI: "Verify if both sides of the final formula resolve to identical dimensions Math formula: [M L T^{-2}]."
Adopting a disciplined translation pipeline turns intimidating physics problems into manageable mathematical proofs.