{
  "aliases": [
    "rotation-of-a-vector-field",
    "rot"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "0GDNHS9J2X"
    },
    {
      "field": "uses",
      "target": "0H6DP8CHND"
    }
  ],
  "body": "\n## Summary\n\nThe curl of a differentiable [[vector field|0299VCW1TH]] in $\\mathbb{R}^3$ is a vector field that measures the rotation of the field at each point.\nIts direction is the axis of the strongest rotation, by the right-hand rule, and its length measures the rate of rotation.\n",
  "commit": "545acf83a9b75c8ddc375ef8b23d2ae101a4d7e4",
  "front": {
    "aliases": [
      "rotation-of-a-vector-field",
      "rot"
    ],
    "kind": "concept",
    "msc": [
      "26B12"
    ],
    "name": "Curl",
    "same_as": {
      "wikidata": "Q206310",
      "wikipedia": "Curl (mathematics)"
    },
    "sources": [
      {
        "locator": "Definition",
        "url": "https://en.wikipedia.org/wiki/Curl_(mathematics)"
      }
    ],
    "tag": "0NF6GQNXMY",
    "uses": [
      "0299VCW1TH",
      "09EGC6F8PT"
    ]
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0NF6GQNXMY/",
  "links": [
    {
      "field": "uses",
      "target": "0299VCW1TH"
    },
    {
      "field": "uses",
      "target": "09EGC6F8PT"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0NF6GQNXMY.md",
  "msc": [
    "26B12"
  ],
  "name": "Curl",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0NF/0NF6GQNXMY.md",
  "status": null,
  "tag": "0NF6GQNXMY",
  "uri": "m2://0NF6GQNXMY",
  "url": "https://math2.tamnd.com/wiki/curl/",
  "writing": {
    "tag": "0NF6GQNXMY",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}
