311 lines
9.7 KiB
HTML
311 lines
9.7 KiB
HTML
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<title>Torque Law • stream.4ort.net</title>
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<script defer src="https://analytics.4ort.xyz/script.js" data-website-id="d3ed927c-888a-4a6c-ae5f-0b1c613ddf5b"></script>
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</head>
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<body>
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<div class="container">
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<header>
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<h1>TORQUE LAW</h1>
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<div class="subtitle">Q48103 // Q7826786 — THE PHYSICS OF THE HUB</div>
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<p>Antonio built the altar. 140 ft-lbs, star pattern, three passes. Not ritual. Engineering.</p>
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</header>
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<section>
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<h2>I. DEFINITION BY ENTITY</h2>
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<div class="definition-box">
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<p><strong>Q48103 (torque)</strong>:<br>
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Tendency of a force to rotate an object; counterpart of force in rotational systems.<br>
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<span class="dimension">SI unit: newton metre (N·m)</span></p>
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<p style="margin-top: 1rem;"><strong>Q7826786 (torque-to-yield-fastener)</strong>:<br>
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Type of fastener tightened to plastic deformation zone for controlled clamping force.</p>
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</div>
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<p>Torque is not a metaphor. It is a measurable physical quantity. ISO 80000-4:2006 defines it. The Wikidata graph binds the concept to the standard.</p>
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</section>
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<section>
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<h2>II. THE CORE EQUATION</h2>
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<div class="equation">
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τ = r × F × sin(θ)
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</div>
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<table class="variable-table">
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<tr>
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<td class="var-name">τ</td>
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<td>Torque magnitude</td>
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<td class="var-unit">N·m (newton metres)</td>
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</tr>
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<tr>
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<td class="var-name">r</td>
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<td>Lever arm length (distance from pivot)</td>
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<td class="var-unit">m (metres)</td>
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</tr>
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<tr>
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<td class="var-name">F</td>
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<td>Applied force magnitude</td>
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<td class="var-unit">N (newtons)</td>
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</tr>
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<tr>
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<td class="var-name">θ</td>
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<td>Angle between force vector and lever arm</td>
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<td class="var-unit">rad (radians)</td>
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</tr>
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</table>
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<p>For orthogonal application (θ = 90°, sin(90°) = 1):</p>
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<div class="equation">
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τ = r × F
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</div>
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</section>
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<section>
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<h2>III. THE ALTAR SPECIFICATION</h2>
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<p>Antonio's sequence encodes the physics:</p>
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<ul style="font-family: monospace; line-height: 1.8;">
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<li><strong>140 ft-lbs</strong> = 189.8 N·m (target torque)</li>
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<li><strong>star pattern</strong> = sequential loading to distribute clamping force evenly across flange</li>
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<li><strong>three passes</strong> = incremental tightening to avoid elastic deformation before yield point</li>
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</ul>
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<p>This is not poetry. It is the stress distribution algorithm executed in steel.</p>
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<img src="https://images.pexels.com/photos/30496227/pexels-photo-30496227.jpeg?auto=compress&cs=tinysrgb&dpr=2&h=650&w=940" alt="Steel hex bolts in bulk — industrial fasteners ready for torque specification">
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</section>
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<section>
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<h2>IV. TORQUE CALCULATOR</h2>
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<div class="calc-box">
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<p style="margin-top: 0; font-family: monospace; color: var(--accent);">// COMPUTE LEVER ARM FOR TARGET TORQUE</p>
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<div class="calc-input">
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<label for="force">Force (N):</label>
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<input type="number" id="force" placeholder="e.g., 500" step="any">
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</div>
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<div class="calc-input">
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<label for="torque">Target Torque (N·m):</label>
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<input type="number" id="torque" placeholder="e.g., 189.8" step="any">
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</div>
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<button class="calc-btn" onclick="calculateLever()">COMPUTE LEVER ARM</button>
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<div class="calc-result" id="result">
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<!-- Result will appear here -->
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</div>
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<p style="margin-top: 1rem; font-size: 0.8rem; opacity: 0.6; font-family: monospace;">
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Formula: r = τ ÷ F (for θ = 90°)<br>
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Source: ISO 80000-4:2006, Wikidata Q48103
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</p>
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</div>
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</section>
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<section>
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<h2>V. RENDER FARM PARALLEL</h2>
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<p>The same law governs the cluster. Each GPU is a fastener. Each node applies torque to the render queue. Aggregate throughput is the sum of individual torques applied in parallel.</p>
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<p>See <a class="link-ref" href="render-farm-theory.html">Law of the Hub</a> for the computational equivalent.</p>
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</section>
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<div class="citation">
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SOURCE: Wikidata Q48103 (torque), Q7826786 (torque-to-yield-fastener) — CC0<br>
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STANDARD: ISO 80000-4:2006 Quantities and units—Part 4: Mechanics<br>
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RELATED: render-farm-theory.html | render-farm-calculator.html
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</div>
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<nav class="nav">
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<a href="index.html">INDEX</a>
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<a href="render-farm-architecture.html">ARCHITECTURE</a>
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<a href="render-farm-spec.html">SPECIFICATION</a>
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<a href="render-farm-theory.html">THEORY</a>
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<a href="render-farm-calculator.html">CALCULATOR</a>
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</nav>
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</div>
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<script>
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function calculateLever() {
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const force = parseFloat(document.getElementById('force').value);
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const torque = parseFloat(document.getElementById('torque').value);
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if (isNaN(force) || isNaN(torque)) {
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document.getElementById('result').innerHTML = '<span style="color: #ff6b6b;">ERROR: Both inputs required</span>';
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return;
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}
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if (force === 0) {
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document.getElementById('result').innerHTML = '<span style="color: #ff6b6b;">ERROR: Force cannot be zero (division by zero)</span>';
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return;
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}
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const leverArm = torque / force;
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let resultHtml = `<strong>r = ${leverArm.toFixed(4)} m</strong>`;
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resultHtml += `<br><span style="opacity: 0.7;">// Lever arm required for ${torque} N·m with ${force} N force</span>`;
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// Also show in inches for practical use
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const inches = leverArm * 39.3701;
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resultHtml += `<br><span style="opacity: 0.7;">// ≈ ${inches.toFixed(2)} inches</span>`;
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document.getElementById('result').innerHTML = resultHtml;
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}
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</script>
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</body>
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</html>
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