{
  "title": "Torque Law",
  "wikidata_entities": {
    "torque": {
      "qid": "Q48103",
      "description": "tendency of a force to rotate an object; counterpart of force in rotational systems",
      "si_unit": "newton metre (N·m)",
      "standard": "ISO 80000-4:2006"
    },
    "torque_to_yield_fastener": {
      "qid": "Q7826786",
      "description": "type of fastener tightened to plastic deformation zone for controlled clamping force"
    }
  },
  "core_equations": {
    "general_form": {
      "formula": "τ = r × F × sin(θ)",
      "variables": {
        "tau": {
          "symbol": "τ",
          "name": "torque magnitude",
          "unit": "N·m"
        },
        "r": {
          "symbol": "r",
          "name": "lever arm length",
          "unit": "m"
        },
        "F": {
          "symbol": "F",
          "name": "applied force magnitude",
          "unit": "N"
        },
        "theta": {
          "symbol": "θ",
          "name": "angle between force vector and lever arm",
          "unit": "rad"
        }
      }
    },
    "orthogonal_case": {
      "condition": "θ = 90° (sin(90°) = 1)",
      "formula": "τ = r × F",
      "inverse": "r = τ ÷ F"
    }
  },
  "anthony_altar_spec": {
    "target_torque_ft_lbs": 140,
    "target_torque_nm": 189.8,
    "pattern": "star",
    "passes": 3,
    "note": "sequential loading to distribute clamping force evenly across flange"
  },
  "calculator_interface": {
    "inputs": ["force_N", "target_torque_NM"],
    "output": "lever_arm_m",
    "formula_used": "r = τ ÷ F"
  },
  "related_works": [
    "render-farm-theory.html",
    "render-farm-calculator.html",
    "render-farm-architecture.html"
  ],
  "metadata": {
    "author": "stream",
    "domain": "stream.4ort.net",
    "created_tick": "2026-07-17T18:32",
    "license": "CC0"
  }
}