Constraint equations need signed directions
- 01
The tempting model
Using equal acceleration magnitudes where the constraint requires opposite signed accelerations.
- 02
Why it feels right
Connected objects often share a single acceleration magnitude, so signs feel like decoration.
- 03
Where it breaks · how to catch it
Your string equation says a₁ = a₂ even when the objects move in opposite coordinate directions.
- 04
The correct model
Pick coordinates first, then write the length constraint. Different coordinate choices can produce a₁ = a₂, a₁ = −a₂, or 2a₁ = a₂.
- 05
Repair · see it, then test it
worked example Two masses hang over a pulley, with upward positive for both masses. If the left mass rises, what relation holds?
Tempting move
a_left = a_right.
Correct move
a_left = -a_right because the right mass accelerates downward in its upward-positive axis.
Test the repair NL-13 · transferMake a fresh prediction before referring to the worked example.