<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <title>Angular Velocity and Tangential Speed</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      width: 100%;
      height: 100%;
      background: #ffffff;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 12px;
      user-select: none;
    }

    /* Comparison Badges */
    .summary-row {
      display: flex;
      flex-wrap: wrap;
      justify-content: center;
      gap: 8px;
      width: 100%;
      max-width: 440px;
    }
    .badge {
      display: inline-flex;
      align-items: center;
      gap: 6px;
      padding: 5px 10px;
      border-radius: 6px;
      font-size: 13px;
      font-weight: 600;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
    }
    .badge-blue {
      color: #0284c7;
      background: #f0f9ff;
      border-color: #bae6fd;
    }
    .badge-orange {
      color: #ea580c;
      background: #fff7ed;
      border-color: #fed7aa;
    }

    /* Turntable SVG Container */
    .canvas-wrap {
      width: 100%;
      max-width: 360px;
      flex: 1;
      display: flex;
      align-items: center;
      justify-content: center;
      position: relative;
    }
    svg {
      width: 100%;
      height: auto;
      max-height: 340px;
      overflow: visible;
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      width: 100%;
      padding-top: 4px;
    }
    .btn {
      appearance: none;
      border: 1px solid #cbd5e1;
      background: #f8fafc;
      color: #1e2945;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 14px;
      border-radius: 6px;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 4px;
      transition: background 0.2s, border-color 0.2s;
    }
    .btn:active {
      background: #e2e8f0;
    }
    .btn-active {
      background: #0284c7;
      border-color: #0284c7;
      color: #ffffff;
    }
  </style>
</head>
<body>

  
  <div class="summary-row">
    <div class="badge badge-blue">
      <span>Radius:</span>
      <span>r vs 2r</span>
    </div>
    <div class="badge">
      <span>Same <span style="font-style:italic;">ω</span></span>
    </div>
    <div class="badge badge-orange">
      <span>v<sub>B</sub> = 2 × v<sub>A</sub></span>
    </div>
  </div>

  
  <div class="canvas-wrap">
    <svg viewBox="0 0 360 360">
      <defs>
        
        <marker id="arrow-v" viewBox="0 0 8 8" refX="6" refY="4" markerWidth="6" markerHeight="6" orient="auto">
          <path d="M 0 1 L 8 4 L 0 7 z" fill="#ea580c" />
        </marker>
        
        <marker id="arrow-rot" viewBox="0 0 6 6" refX="5" refY="3" markerWidth="5" markerHeight="5" orient="auto">
          <path d="M 0 1 L 6 3 L 0 5 z" fill="#0284c7" />
        </marker>
      </defs>

      
      <circle cx="180" cy="180" r="162" fill="#f8fafc" stroke="#e2e8f0" stroke-width="2" />
      
      
      <circle cx="180" cy="180" r="70" fill="none" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="4 4" />
      <circle cx="180" cy="180" r="140" fill="none" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="4 4" />

      
      <g id="turntableGroup" transform="rotate(0 180 180)">
        
        <line x1="180" y1="180" x2="320" y2="180" stroke="#0284c7" stroke-width="3" stroke-linecap="round" />
        
        
        <text x="215" y="172" fill="#0284c7" font-size="12" font-weight="700" text-anchor="middle">r</text>
        <text x="285" y="172" fill="#0284c7" font-size="12" font-weight="700" text-anchor="middle">2r</text>

        
        <circle cx="250" cy="180" r="6" fill="#0284c7" stroke="#ffffff" stroke-width="2" />
        <text x="250" y="198" fill="#1e2945" font-size="12" font-weight="800" text-anchor="middle">A</text>

        
        <line x1="250" y1="180" x2="250" y2="136" stroke="#ea580c" stroke-width="3.5" stroke-linecap="round" marker-end="url(#arrow-v)" />
        <text x="242" y="130" fill="#ea580c" font-size="12" font-weight="700" text-anchor="end">v<tspan font-size="10" dy="2">A</tspan><tspan font-size="12" dy="-2"> = ωr</tspan></text>

        
        <circle cx="320" cy="180" r="6" fill="#0284c7" stroke="#ffffff" stroke-width="2" />
        <text x="320" y="198" fill="#1e2945" font-size="12" font-weight="800" text-anchor="middle">B</text>

        
        <line x1="320" y1="180" x2="320" y2="96" stroke="#ea580c" stroke-width="3.5" stroke-linecap="round" marker-end="url(#arrow-v)" />
        <text x="312" y="90" fill="#ea580c" font-size="12" font-weight="700" text-anchor="end">v<tspan font-size="10" dy="2">B</tspan><tspan font-size="12" dy="-2"> = 2ωr</tspan></text>
      </g>

      
      <path d="M 180 152 A 28 28 0 0 0 154 175" fill="none" stroke="#0284c7" stroke-width="2" stroke-linecap="round" marker-end="url(#arrow-rot)" />
      <text x="160" y="162" fill="#0284c7" font-size="14" font-weight="700" font-style="italic">ω</text>

      
      <circle cx="180" cy="180" r="4.5" fill="#475569" />
    </svg>
  </div>

  
  <div class="controls">
    <button class="btn" id="playBtn" aria-label="Toggle Animation">
      <span id="playIcon">⏸</span> Pause
    </button>
    <button class="btn btn-active" id="speedSlow">1×</button>
    <button class="btn" id="speedFast">2×</button>
  </div>

  <script>
    const group = document.getElementById('turntableGroup');
    const playBtn = document.getElementById('playBtn');
    const playIcon = document.getElementById('playIcon');
    const speedSlow = document.getElementById('speedSlow');
    const speedFast = document.getElementById('speedFast');

    let isPlaying = true;
    let baseSpeed = 0.6; // degrees per frame (~60fps = 36 deg/sec -> 10s per lap)
    let speedMultiplier = 1;
    let angle = 0;
    let lastTime = null;

    function animate(currentTime) {
      if (lastTime !== null && isPlaying) {
        const delta = Math.min((currentTime - lastTime) / 16.67, 2);
        angle = (angle + baseSpeed * speedMultiplier * delta) % 360;
        group.setAttribute('transform', `rotate(${angle} 180 180)`);
      }
      lastTime = currentTime;
      requestAnimationFrame(animate);
    }
    requestAnimationFrame(animate);

    playBtn.addEventListener('click', () => {
      isPlaying = !isPlaying;
      playIcon.textContent = isPlaying ? '⏸' : '▶';
      playBtn.childNodes[1].nodeValue = isPlaying ? ' Pause' : ' Play';
    });

    speedSlow.addEventListener('click', () => {
      speedMultiplier = 1;
      speedSlow.classList.add('btn-active');
      speedFast.classList.remove('btn-active');
    });

    speedFast.addEventListener('click', () => {
      speedMultiplier = 2;
      speedFast.classList.add('btn-active');
      speedSlow.classList.remove('btn-active');
    });
  </script>
</body>
</html>

Angular Velocity and Linear Speed in Circular Motion

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      user-select: none;
      -webkit-user-select: none;
    }
    body {
      width: 100%;
      height: 100%;
      background: #ffffff;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 12px;
      color: #1e2945;
    }

    .wheel-container {
      position: relative;
      width: 100%;
      max-width: 420px;
      aspect-ratio: 1 / 1;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    svg.connections {
      position: absolute;
      inset: 0;
      width: 100%;
      height: 100%;
      pointer-events: none;
      z-index: 1;
    }

    /* SVG Path styles */
    .arrow-path {
      fill: none;
      stroke: #e2e8f0;
      stroke-width: 3;
      stroke-linecap: round;
      transition: stroke 0.3s ease, stroke-width 0.3s ease;
    }
    .arrow-path.active {
      stroke: #0284c7;
      stroke-width: 4;
    }

    /* Variable Nodes */
    .node {
      position: absolute;
      width: 82px;
      height: 82px;
      border-radius: 50%;
      background: #ffffff;
      border: 2.5px solid #cbd5e1;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      cursor: pointer;
      z-index: 3;
      transition: border-color 0.25s ease, box-shadow 0.25s ease, transform 0.25s ease;
      box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);
    }
    .node:hover {
      box-shadow: 0 6px 16px rgba(2, 132, 199, 0.18);
    }
    .node.active {
      border-color: #0284c7;
      box-shadow: 0 0 0 4px rgba(2, 132, 199, 0.15), 0 6px 16px rgba(2, 132, 199, 0.2);
    }

    .node-sym {
      font-size: 22px;
      font-weight: 700;
      line-height: 1.1;
      color: #0f172a;
      font-style: italic;
      font-family: "Times New Roman", Times, serif;
    }
    .node-unit {
      font-size: 11px;
      font-weight: 700;
      color: #64748b;
      margin-top: 2px;
      background: #f1f5f9;
      padding: 1px 6px;
      border-radius: 4px;
    }
    .node.active .node-unit {
      background: #e0f2fe;
      color: #0369a1;
    }

    /* Positions (Circular Layout) */
    .pos-top    { top: 4%;  left: 50%; transform: translateX(-50%); }
    .pos-right  { top: 50%; right: 4%; transform: translateY(-50%); }
    .pos-bottom { bottom: 4%; left: 50%; transform: translateX(-50%); }
    .pos-left   { top: 50%; left: 4%;  transform: translateY(-50%); }

    /* Transition Formula Badges */
    .formula-badge {
      position: absolute;
      z-index: 4;
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      padding: 5px 10px;
      border-radius: 20px;
      font-size: 13px;
      font-weight: 700;
      color: #334155;
      cursor: pointer;
      box-shadow: 0 2px 6px rgba(0,0,0,0.05);
      transition: all 0.25s ease;
      white-space: nowrap;
    }
    .formula-badge:hover {
      box-shadow: 0 4px 10px rgba(0,0,0,0.1);
    }
    .formula-badge.active {
      border-color: #0284c7;
      background: #f0f9ff;
      color: #0369a1;
      box-shadow: 0 0 0 3px rgba(2, 132, 199, 0.15);
    }

    .fb-tr { top: 22%; right: 17%; }
    .fb-br { bottom: 22%; right: 17%; }
    .fb-bl { bottom: 22%; left: 17%; }
    .fb-tl { top: 22%; left: 17%; }

    /* Center Info Card */
    .center-hub {
      position: absolute;
      width: 130px;
      height: 130px;
      border-radius: 50%;
      background: #f8fafc;
      border: 1.5px dashed #cbd5e1;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      text-align: center;
      z-index: 2;
      padding: 8px;
    }
    .hub-title {
      font-size: 11px;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      font-weight: 800;
      color: #64748b;
      margin-bottom: 2px;
    }
    .hub-eq {
      font-size: 15px;
      font-weight: 700;
      color: #0f172a;
      font-family: "Times New Roman", Times, serif;
      font-style: italic;
    }
    .hub-mult {
      font-size: 11px;
      font-weight: 600;
      color: #0284c7;
      margin-top: 2px;
    }

    /* Bottom Stepper / Nav */
    .nav-bar {
      display: flex;
      align-items: center;
      gap: 8px;
      margin-top: 10px;
    }
    .nav-btn {
      background: #f1f5f9;
      border: 1px solid #e2e8f0;
      border-radius: 6px;
      width: 32px;
      height: 32px;
      font-size: 14px;
      color: #334155;
      display: flex;
      align-items: center;
      justify-content: center;
      cursor: pointer;
      transition: background 0.2s;
    }
    .nav-btn:hover {
      background: #e2e8f0;
    }
    .step-dots {
      display: flex;
      gap: 6px;
    }
    .dot {
      width: 8px;
      height: 8px;
      border-radius: 50%;
      background: #cbd5e1;
      cursor: pointer;
      transition: background 0.2s, transform 0.2s;
    }
    .dot.active {
      background: #0284c7;
      transform: scale(1.25);
    }
  </style>
</head>
<body>

  <div class="wheel-container">
    <svg class="connections" viewBox="0 0 400 400">
      <defs>
        <marker id="arrow" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 1 2 L 8 5 L 1 8 z" fill="#cbd5e1" id="arrow-head-default" />
        </marker>
        <marker id="arrow-active" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 1 2 L 8 5 L 1 8 z" fill="#0284c7" />
        </marker>
      </defs>

      
      
      <path id="path-0" class="arrow-path" d="M 235 55 A 150 150 0 0 1 345 165" marker-end="url(#arrow)" />
      
      
      <path id="path-1" class="arrow-path" d="M 345 235 A 150 150 0 0 1 235 345" marker-end="url(#arrow)" />
      
      
      <path id="path-2" class="arrow-path" d="M 165 345 A 150 150 0 0 1 55 235" marker-end="url(#arrow)" />
      
      
      <path id="path-3" class="arrow-path" d="M 55 165 A 150 150 0 0 1 165 55" marker-end="url(#arrow)" />
    </svg>

    
    <div class="center-hub">
      <div class="hub-title" id="hubTitle">Transition</div>
      <div class="hub-eq" id="hubEq">f = 1 / T</div>
      <div class="hub-mult" id="hubDesc">Invert Period</div>
    </div>

    
    <div class="node pos-top active" id="node-0" onclick="setStep(0)">
      <span class="node-sym">T</span>
      <span class="node-unit">s</span>
    </div>

    <div class="node pos-right" id="node-1" onclick="setStep(1)">
      <span class="node-sym">f</span>
      <span class="node-unit">Hz</span>
    </div>

    <div class="node pos-bottom" id="node-2" onclick="setStep(2)">
      <span class="node-sym">ω</span>
      <span class="node-unit">rad/s</span>
    </div>

    <div class="node pos-left" id="node-3" onclick="setStep(3)">
      <span class="node-sym">v</span>
      <span class="node-unit">m/s</span>
    </div>

    
    <div class="formula-badge fb-tr active" id="fb-0" onclick="setStep(0)">
      f = 1/T
    </div>

    <div class="formula-badge fb-br" id="fb-1" onclick="setStep(1)">
      ω = 2π f
    </div>

    <div class="formula-badge fb-bl" id="fb-2" onclick="setStep(2)">
      v = ω · r
    </div>

    <div class="formula-badge fb-tl" id="fb-3" onclick="setStep(3)">
      T = 2πr / v
    </div>
  </div>

  
  <div class="nav-bar">
    <button class="nav-btn" onclick="prevStep()">❮</button>
    <div class="step-dots">
      <div class="dot active" onclick="setStep(0)"></div>
      <div class="dot" onclick="setStep(1)"></div>
      <div class="dot" onclick="setStep(2)"></div>
      <div class="dot" onclick="setStep(3)"></div>
    </div>
    <button class="nav-btn" onclick="nextStep()">❯</button>
  </div>

  <script>
    const steps = [
      {
        from: 0,
        to: 1,
        eq: 'f = 1 / T',
        desc: 'Reciprocal',
        title: 'T → f'
      },
      {
        from: 1,
        to: 2,
        eq: 'ω = 2π f',
        desc: 'Multiply 2π',
        title: 'f → ω'
      },
      {
        from: 2,
        to: 3,
        eq: 'v = ω · r',
        desc: 'Multiply radius',
        title: 'ω → v'
      },
      {
        from: 3,
        to: 0,
        eq: 'T = 2πr / v',
        desc: 'Distance / Speed',
        title: 'v → T'
      }
    ];

    let currentStep = 0;
    let autoTimer = null;

    function updateUI() {
      const data = steps[currentStep];

      // Nodes
      for (let i = 0; i < 4; i++) {
        const node = document.getElementById(`node-${i}`);
        node.classList.toggle('active', i === data.from || i === data.to);
      }

      // Formula Badges
      for (let i = 0; i < 4; i++) {
        const fb = document.getElementById(`fb-${i}`);
        fb.classList.toggle('active', i === currentStep);
      }

      // SVG Paths
      for (let i = 0; i < 4; i++) {
        const path = document.getElementById(`path-${i}`);
        if (i === currentStep) {
          path.classList.add('active');
          path.setAttribute('marker-end', 'url(#arrow-active)');
        } else {
          path.classList.remove('active');
          path.setAttribute('marker-end', 'url(#arrow)');
        }
      }

      // Dots
      document.querySelectorAll('.dot').forEach((dot, idx) => {
        dot.classList.toggle('active', idx === currentStep);
      });

      // Hub
      document.getElementById('hubTitle').textContent = data.title;
      document.getElementById('hubEq').textContent = data.eq;
      document.getElementById('hubDesc').textContent = data.desc;
    }

    function setStep(idx) {
      currentStep = (idx + 4) % 4;
      updateUI();
      resetTimer();
    }

    function nextStep() {
      setStep(currentStep + 1);
    }

    function prevStep() {
      setStep(currentStep - 1);
    }

    function resetTimer() {
      clearInterval(autoTimer);
      autoTimer = setInterval(() => {
        currentStep = (currentStep + 1) % 4;
        updateUI();
      }, 3500);
    }

    updateUI();
    resetTimer();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      user-select: none;
    }

    .formula-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      font-size: 16px;
      font-weight: 700;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 6px 14px;
      flex-wrap: wrap;
    }

    .badge-s { color: #ea580c; background: #ffedd5; padding: 2px 8px; border-radius: 6px; }
    .badge-r { color: #0284c7; background: #e0f2fe; padding: 2px 8px; border-radius: 6px; }
    .badge-t { color: #7c3aed; background: #ede9fe; padding: 2px 8px; border-radius: 6px; }

    .canvas-container {
      position: relative;
      width: 100%;
      max-width: 320px;
      aspect-ratio: 1 / 1;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }

    .controls {
      width: 100%;
      max-width: 340px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .slider-row {
      display: flex;
      align-items: center;
      gap: 10px;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
    }

    input[type="range"] {
      flex: 1;
      accent-color: #7c3aed;
      cursor: pointer;
      height: 6px;
    }

    .btn-group {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 6px;
    }

    button {
      font-family: inherit;
      font-size: 12px;
      font-weight: 600;
      padding: 7px 4px;
      border-radius: 8px;
      border: 1px solid #cbd5e1;
      background: #ffffff;
      color: #334155;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    button:hover {
      background: #f1f5f9;
    }

    button.active {
      background: #7c3aed;
      color: #ffffff;
      border-color: #7c3aed;
      box-shadow: 0 2px 6px rgba(124, 58, 237, 0.25);
    }
  </style>
</head>
<body>

  
  <div class="formula-row">
    <span class="badge-s" id="sFormula">s = 1.0 r</span>
    <span>=</span>
    <span class="badge-r">r</span>
    <span>·</span>
    <span class="badge-t" id="tFormula">θ = 1.0 rad (57.3°)</span>
  </div>

  
  <div class="canvas-container">
    <svg viewBox="0 0 300 300">
      
      <circle cx="150" cy="150" r="105" fill="none" stroke="#e2e8f0" stroke-width="2" stroke-dasharray="4 4" />
      
      
      <path id="sector" fill="rgba(124, 58, 237, 0.08)" />

      
      <line x1="150" y1="150" x2="255" y2="150" stroke="#0284c7" stroke-width="3" stroke-linecap="round" />
      <text x="202" y="170" fill="#0284c7" font-size="14" font-weight="700" text-anchor="middle">r</text>

      
      <line id="radiusArm" x1="150" y1="150" x2="255" y2="150" stroke="#0284c7" stroke-width="3" stroke-linecap="round" />

      
      <path id="angleArc" fill="none" stroke="#7c3aed" stroke-width="2.5" />
      <text id="angleLabel" x="182" y="140" fill="#7c3aed" font-size="13" font-weight="700" text-anchor="middle">θ</text>

      
      <circle cx="150" cy="150" r="4.5" fill="#1e293b" />

      
      <path id="arcS" fill="none" stroke="#ea580c" stroke-width="5" stroke-linecap="round" />
      
      
      <text id="arcLabel" fill="#ea580c" font-size="14" font-weight="700" text-anchor="middle">s</text>
    </svg>
  </div>

  
  <div class="controls">
    <div class="slider-row">
      <span>0</span>
      <input type="range" id="angleSlider" min="0.1" max="6.283" step="0.01" value="1.0">
      <span>2π</span>
    </div>
    <div class="btn-group">
      <button id="btn1" class="active">1 rad (s = r)</button>
      <button id="btnPi">π rad (180°)</button>
      <button id="btn2Pi">2π rad (360°)</button>
    </div>
  </div>

  <script>
    const slider = document.getElementById('angleSlider');
    const btn1 = document.getElementById('btn1');
    const btnPi = document.getElementById('btnPi');
    const btn2Pi = document.getElementById('btn2Pi');
    const btns = [btn1, btnPi, btn2Pi];

    const sector = document.getElementById('sector');
    const radiusArm = document.getElementById('radiusArm');
    const angleArc = document.getElementById('angleArc');
    const angleLabel = document.getElementById('angleLabel');
    const arcS = document.getElementById('arcS');
    const arcLabel = document.getElementById('arcLabel');
    const sFormula = document.getElementById('sFormula');
    const tFormula = document.getElementById('tFormula');

    const CX = 150, CY = 150, R = 105, AR = 38;

    function update(theta) {
      // Clamp for full circle boundary rendering
      const isFull = theta >= 6.27;
      const angle = isFull ? 6.28318 : theta;
      const deg = (angle * (180 / Math.PI)).toFixed(1);
      const rad = angle.toFixed(2);
      const sFactor = angle.toFixed(2);

      // Math coordinates (SVG y goes down)
      const cos = Math.cos(angle);
      const sin = Math.sin(angle);
      const endX = CX + R * cos;
      const endY = CY - R * sin;

      // Update Radius Arm
      radiusArm.setAttribute('x2', endX);
      radiusArm.setAttribute('y2', endY);

      // Large arc flag
      const largeArc = angle > Math.PI ? 1 : 0;

      // Arc path s
      if (isFull) {
        arcS.setAttribute('d', `M ${CX + R} ${CY} A ${R} ${R} 0 1 0 ${CX + R - 0.01} ${CY}`);
        sector.setAttribute('d', `M ${CX} ${CY} m -${R}, 0 a ${R},${R} 0 1,0 ${R * 2},0 a ${R},${R} 0 1,0 -${R * 2},0`);
      } else {
        arcS.setAttribute('d', `M ${CX + R} ${CY} A ${R} ${R} 0 ${largeArc} 0 ${endX} ${endY}`);
        sector.setAttribute('d', `M ${CX} ${CY} L ${CX + R} ${CY} A ${R} ${R} 0 ${largeArc} 0 ${endX} ${endY} Z`);
      }

      // Arc label s position
      const midAngle = angle / 2;
      const labelR = R + 18;
      const labelX = CX + labelR * Math.cos(midAngle);
      const labelY = CY - labelR * Math.sin(midAngle) + 5;
      arcLabel.setAttribute('x', labelX);
      arcLabel.setAttribute('y', labelY);
      arcLabel.textContent = Math.abs(angle - 1.0) < 0.05 ? 's = r' : 's';

      // Inner angle arc
      const arcEndX = CX + AR * cos;
      const arcEndY = CY - AR * sin;
      if (isFull) {
        angleArc.setAttribute('d', `M ${CX + AR} ${CY} A ${AR} ${AR} 0 1 0 ${CX + AR - 0.01} ${CY}`);
      } else {
        angleArc.setAttribute('d', `M ${CX + AR} ${CY} A ${AR} ${AR} 0 ${largeArc} 0 ${arcEndX} ${arcEndY}`);
      }

      // Angle label position
      const angleLabelR = Math.min(AR + 18, 52);
      angleLabel.setAttribute('x', CX + angleLabelR * Math.cos(midAngle));
      angleLabel.setAttribute('y', CY - angleLabelR * Math.sin(midAngle) + 4);

      // Formula bar updates
      sFormula.textContent = `s = ${sFactor} r`;
      tFormula.textContent = `θ = ${rad} rad (${deg}°)`;

      // Slider sync
      slider.value = angle;

      // Button active states
      btns.forEach(b => b.classList.remove('active'));
      if (Math.abs(angle - 1.0) < 0.06) btn1.classList.add('active');
      else if (Math.abs(angle - Math.PI) < 0.06) btnPi.classList.add('active');
      else if (isFull) btn2Pi.classList.add('active');
    }

    slider.addEventListener('input', (e) => update(parseFloat(e.target.value)));

    btn1.addEventListener('click', () => update(1.0));
    btnPi.addEventListener('click', () => update(Math.PI));
    btn2Pi.addEventListener('click', () => update(6.28318));

    // Initialize at 1 Radian
    update(1.0);
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      width: 100%;
      min-height: 100%;
      background: #ffffff;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 10px 12px 14px;
      user-select: none;
      -webkit-user-select: none;
    }

    .top-badge {
      display: inline-flex;
      align-items: center;
      gap: 8px;
      background: #eff6ff;
      border: 1px solid #bfdbfe;
      padding: 5px 14px;
      border-radius: 20px;
      font-size: 14px;
      font-weight: 700;
      color: #1d4ed8;
      margin-bottom: 6px;
    }
    .top-badge span {
      color: #475569;
      font-weight: 500;
    }

    .canvas-container {
      position: relative;
      width: 100%;
      max-width: 620px;
      flex: 1;
      min-height: 240px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    canvas {
      width: 100%;
      height: 100%;
      display: block;
    }

    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      margin-top: 6px;
      width: 100%;
    }

    .btn {
      background: #f8fafc;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
      padding: 6px 14px;
      font-size: 13px;
      font-weight: 600;
      color: #334155;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 5px;
      transition: background 0.2s, border-color 0.2s;
    }
    .btn:active {
      background: #e2e8f0;
    }
    .btn.active {
      background: #2563eb;
      border-color: #2563eb;
      color: #ffffff;
    }
  </style>
</head>
<body>

  <div class="top-badge">
    <span>Circular</span> ω <span>=</span> Oscillator ω
  </div>

  <div class="canvas-container">
    <canvas id="simCanvas"></canvas>
  </div>

  <div class="controls">
    <button class="btn" id="playBtn">⏸ Pause</button>
    <button class="btn" id="spd1">1×</button>
    <button class="btn active" id="spd2">2×</button>
    <button class="btn" id="resetBtn">↺ Reset</button>
  </div>

  <script>
    const canvas = document.getElementById('simCanvas');
    const ctx = canvas.getContext('2d');
    const playBtn = document.getElementById('playBtn');
    const resetBtn = document.getElementById('resetBtn');
    const spd1Btn = document.getElementById('spd1');
    const spd2Btn = document.getElementById('spd2');

    let isPlaying = true;
    let speed = 1.5;
    let theta = 0;
    let lastTime = performance.now();

    function resize() {
      const rect = canvas.getBoundingClientRect();
      const dpr = window.devicePixelRatio || 1;
      canvas.width = rect.width * dpr;
      canvas.height = rect.height * dpr;
      ctx.resetTransform();
      ctx.scale(dpr, dpr);
    }
    window.addEventListener('resize', resize);
    resize();

    function draw() {
      const w = canvas.getBoundingClientRect().width;
      const h = canvas.getBoundingClientRect().height;

      ctx.clearRect(0, 0, w, h);

      // Layout geometry
      const isMobile = w < 440;
      const R = Math.min(h * 0.32, isMobile ? 48 : 62);
      const cx = isMobile ? R + 22 : R + 40;
      const cy = h * 0.5;

      const trackX = cx + R + (isMobile ? 18 : 28);
      const waveStartX = trackX + (isMobile ? 14 : 20);
      const waveEndX = w - 16;

      // 1. CIRCLE (Left)
      // Axes
      ctx.strokeStyle = '#e2e8f0';
      ctx.lineWidth = 1.5;
      ctx.setLineDash([4, 4]);
      ctx.beginPath();
      ctx.moveTo(cx - R - 12, cy);
      ctx.lineTo(cx + R + 12, cy);
      ctx.moveTo(cx, cy - R - 12);
      ctx.lineTo(cx, cy + R + 12);
      ctx.stroke();

      // Main Circle
      ctx.setLineDash([]);
      ctx.strokeStyle = '#cbd5e1';
      ctx.lineWidth = 2;
      ctx.beginPath();
      ctx.arc(cx, cy, R, 0, Math.PI * 2);
      ctx.stroke();

      // Current rotating particle position
      const px = cx + R * Math.cos(theta);
      const py = cy - R * Math.sin(theta);

      // Angle sector / arc (ωt)
      ctx.fillStyle = 'rgba(37, 99, 235, 0.08)';
      ctx.beginPath();
      ctx.moveTo(cx, cy);
      ctx.arc(cx, cy, R * 0.38, 0, - (theta % (Math.PI * 2)), true);
      ctx.closePath();
      ctx.fill();

      // Radius Vector A
      ctx.strokeStyle = '#2563eb';
      ctx.lineWidth = 2.5;
      ctx.beginPath();
      ctx.moveTo(cx, cy);
      ctx.lineTo(px, py);
      ctx.stroke();

      // Radius Label "A"
      const midAngle = theta;
      const labelDist = R * 0.55;
      const lx = cx + labelDist * Math.cos(midAngle) + 8 * Math.sin(midAngle);
      const ly = cy - labelDist * Math.sin(midAngle) + 8 * Math.cos(midAngle);
      ctx.fillStyle = '#2563eb';
      ctx.font = 'bold 13px system-ui';
      ctx.textAlign = 'center';
      ctx.textBaseline = 'middle';
      ctx.fillText('A', lx, ly);

      // Particle on Circle
      ctx.fillStyle = '#2563eb';
      ctx.beginPath();
      ctx.arc(px, py, 6, 0, Math.PI * 2);
      ctx.fill();

      // Title: Circular Motion
      ctx.fillStyle = '#64748b';
      ctx.font = '600 12px system-ui';
      ctx.fillText('Circular Motion', cx, cy + R + 24);

      // 2. LINEAR OSCILLATOR (Middle Track)
      // Track line [-A, +A]
      ctx.strokeStyle = '#94a3b8';
      ctx.lineWidth = 3;
      ctx.lineCap = 'round';
      ctx.beginPath();
      ctx.moveTo(trackX, cy - R);
      ctx.lineTo(trackX, cy + R);
      ctx.stroke();

      // Amplitude ticks
      ctx.lineWidth = 2;
      ctx.beginPath();
      ctx.moveTo(trackX - 4, cy - R);
      ctx.lineTo(trackX + 4, cy - R);
      ctx.moveTo(trackX - 4, cy + R);
      ctx.lineTo(trackX + 4, cy + R);
      ctx.moveTo(trackX - 3, cy);
      ctx.lineTo(trackX + 3, cy);
      ctx.stroke();

      // Track Labels
      ctx.fillStyle = '#64748b';
      ctx.font = '11px system-ui';
      ctx.textAlign = 'right';
      ctx.fillText('+A', trackX - 6, cy - R + 3);
      ctx.fillText('0', trackX - 6, cy + 3);
      ctx.fillText('−A', trackX - 6, cy + R + 3);

      // Linear projection particle
      ctx.fillStyle = '#0284c7';
      ctx.beginPath();
      ctx.arc(trackX, py, 6, 0, Math.PI * 2);
      ctx.fill();

      // 3. PROJECTION GUIDE LINE (Horizontal dashed)
      ctx.strokeStyle = '#f59e0b';
      ctx.lineWidth = 1.8;
      ctx.setLineDash([4, 3]);
      ctx.beginPath();
      ctx.moveTo(px, py);
      ctx.lineTo(waveStartX, py);
      ctx.stroke();
      ctx.setLineDash([]);

      // 4. SINE WAVE GRAPH (Right)
      // Wave axis
      ctx.strokeStyle = '#e2e8f0';
      ctx.lineWidth = 1.5;
      ctx.beginPath();
      ctx.moveTo(waveStartX, cy);
      ctx.lineTo(waveEndX, cy);
      ctx.stroke();

      // Bounds (+A / -A lines)
      ctx.strokeStyle = '#f1f5f9';
      ctx.setLineDash([2, 4]);
      ctx.beginPath();
      ctx.moveTo(waveStartX, cy - R);
      ctx.lineTo(waveEndX, cy - R);
      ctx.moveTo(waveStartX, cy + R);
      ctx.lineTo(waveEndX, cy + R);
      ctx.stroke();
      ctx.setLineDash([]);

      // Sine curve trace
      const waveLength = isMobile ? 120 : 160;
      const k = (Math.PI * 2) / waveLength;

      ctx.strokeStyle = '#0284c7';
      ctx.lineWidth = 2.5;
      ctx.beginPath();
      for (let x = waveStartX; x <= waveEndX; x += 2) {
        const dx = x - waveStartX;
        const waveY = cy - R * Math.sin(theta - dx * k);
        if (x === waveStartX) ctx.moveTo(x, waveY);
        else ctx.lineTo(x, waveY);
      }
      ctx.stroke();

      // Wave origin dot
      ctx.fillStyle = '#0284c7';
      ctx.beginPath();
      ctx.arc(waveStartX, py, 4, 0, Math.PI * 2);
      ctx.fill();

      // Title: Simple Harmonic Motion
      ctx.fillStyle = '#64748b';
      ctx.font = '600 12px system-ui';
      ctx.textAlign = 'center';
      const waveMid = (waveStartX + waveEndX) / 2;
      ctx.fillText('Simple Harmonic Motion', waveMid, cy + R + 24);
    }

    function animate(now) {
      const dt = Math.min((now - lastTime) / 1000, 0.1);
      lastTime = now;

      if (isPlaying) {
        theta += speed * dt;
      }

      draw();
      requestAnimationFrame(animate);
    }
    requestAnimationFrame(animate);

    playBtn.addEventListener('click', () => {
      isPlaying = !isPlaying;
      playBtn.textContent = isPlaying ? '⏸ Pause' : '▶ Play';
      playBtn.classList.toggle('active', !isPlaying);
    });

    resetBtn.addEventListener('click', () => {
      theta = 0;
      if (!isPlaying) {
        isPlaying = true;
        playBtn.textContent = '⏸ Pause';
        playBtn.classList.remove('active');
      }
    });

    spd1Btn.addEventListener('click', () => {
      speed = 0.8;
      spd1Btn.classList.add('active');
      spd2Btn.classList.remove('active');
    });

    spd2Btn.addEventListener('click', () => {
      speed = 1.6;
      spd2Btn.classList.add('active');
      spd1Btn.classList.remove('active');
    });
  </script>
</body>
</html>

OGS.13.PS.3

Aligned learning resources

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