Vector Calculus
Math · Advanced · Lesson 7 of 8

Curl

How much it swirls

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

  • Curl = ∂Q/∂x − ∂P/∂y: twice the local spin rate.
  • Straight shear flows can have curl; circling vortices can have none.
  • Gradient fields have zero curl.

Steps

  1. A paddle wheel
  2. Curl of a whirl
  3. Find the calm spot
  4. A whirlpool without spin
  5. Curl of a shear
  6. Curl and potentials