{"job_id":"anim-job-0ded0f4f-fe50-4070-a5e3-6004ceb73511","request_id":"test-physics-newton-1b2ba770-6450-4b1c-a815-8b28db3d7c87-1778704510421","status":"complete","asset":{"primary_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-0ded0f4f-fe50-4070-a5e3-6004ceb73511/walkthrough.mp4","thumbnail_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-0ded0f4f-fe50-4070-a5e3-6004ceb73511/thumb.jpg","transcript_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-0ded0f4f-fe50-4070-a5e3-6004ceb73511/transcript.vtt","interactive_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-0ded0f4f-fe50-4070-a5e3-6004ceb73511/index.html","scenefile_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-0ded0f4f-fe50-4070-a5e3-6004ceb73511/scene-source.json","duration_seconds":15,"byte_size":502631,"renderer":"html_three_js_local","parameters":{"style":"auto","executor":"native_render_executor","localPath":"/app/storage/assets/anim-job-0ded0f4f-fe50-4070-a5e3-6004ceb73511","control_count":2,"interactivity":"none","simulation_id":"physics.11.laws_of_motion.newton_non_inertial","renderer_style":"three_js","durationSeconds":15,"render_manifest":{"jobId":"anim-job-0ded0f4f-fe50-4070-a5e3-6004ceb73511","request":{"gap":{"topic":"newton-second-law-non-inertial","severity":"dangerous","error_type":"wrong_assumption","memory_state":"fragile","display_topic":"Newton 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context.","narration":"Newton Second Law in Non-Inertial Frames"},{"label":"Mistake","visual":"Show the wrong approach and why it seems plausible.","narration":"Applied F=ma in a rotating frame without pseudo force"},{"label":"Correction","visual":"Show the right approach step by step.","narration":"In non-inertial frames, include pseudo force opposite frame acceleration."},{"label":"Concept","visual":"Highlight the key formula and the governing relationship.","narration":"F = ma. pseudo force"}],"title":"Newton Second Law in Non-Inertial Frames","sceneCode":"<!doctype html>\n<html lang=\"en\">\n<head>\n  <meta charset=\"utf-8\"/>\n  <meta name=\"viewport\" content=\"width=device-width, initial-scale=1\"/>\n  <title>Newton's Second Law in Rotating Frames</title>\n  <style>\n    :root{--bg:#0f1418;--panel:#182228;--line:#2e3e46;--accent:#e5ba67;--text:#f4f1ea;--muted:#c8d4da;--blue:#63b3ff;--green:#87e8a8;--red:#de7f76;}\n    *{box-sizing:border-box;}\n    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frames</p>\n    <p class=\"formula\">Wrong: F = ma<br/>Right: F + F_pseudo = ma'</p>\n    <label class=\"control\"><span>Angular velocity ω: <strong id=\"v-omega\">3.0</strong> rad/s</span><input id=\"c-omega\" type=\"range\" min=\"0.5\" max=\"8\" step=\"0.1\" value=\"3.0\"/></label>\n    <label class=\"control\"><span>Applied force F: <strong id=\"v-force\">5.0</strong> N</span><input id=\"c-force\" type=\"range\" min=\"0\" max=\"15\" step=\"0.5\" value=\"5.0\"/></label>\n    <label class=\"control\"><span>Mass m: <strong id=\"v-mass\">1.0</strong> kg</span><input id=\"c-mass\" type=\"range\" min=\"0.5\" max=\"3\" step=\"0.1\" value=\"1.0\"/></label>\n    <ul>\n      <li><strong>Left panel:</strong> Inertial (stationary) frame</li>\n      <li><strong>Right panel:</strong> Rotating frame</li>\n      <li><strong>Green:</strong> Applied force</li>\n      <li><strong>Red:</strong> Pseudo (centrifugal) force</li>\n      <li><strong>Blue:</strong> Net acceleration</li>\n      <li>Without pseudo force in rotating frame: prediction fails!</li>\n    </ul>\n  </aside>\n  <section>\n    <div class=\"stage\" id=\"stage\">\n      <div class=\"legend\" id=\"legend\">Ready</div>\n      <canvas id=\"sim-cv\" style=\"position:absolute;inset:0;width:100%;height:100%;\"></canvas>\n    </div>\n  </section>\n</main>\n<script>\nconst controls = [{\"key\":\"omega\",\"label\":\"Angular velocity\",\"min\":0.5,\"max\":8,\"step\":0.1,\"value\":3.0,\"units\":\"rad/s\"},{\"key\":\"force\",\"label\":\"Applied force\",\"min\":0,\"max\":15,\"step\":0.5,\"value\":5.0,\"units\":\"N\"},{\"key\":\"mass\",\"label\":\"Mass\",\"min\":0.5,\"max\":3,\"step\":0.1,\"value\":1.0,\"units\":\"kg\"}];\nfor(const c of controls){\n  const inp=document.getElementById('c-'+c.key);\n  const out=document.getElementById('v-'+c.key);\n  inp?.addEventListener('input',()=>{out.textContent=inp.value;window.updateModel?.();});\n}\n(function(){\n  const cv=document.getElementById('sim-cv');\n  const ctx=cv.getContext('2d');\n  function resize(){const r=cv.getBoundingClientRect();if(r.width>0){cv.width=r.width;cv.height=r.height;}}\n  resize();new ResizeObserver(resize).observe(cv);\n  let lastTs=0;\n  \n  // State variables\n  let x_inertial = 0, y_inertial = 0;  // Position in inertial frame\n  let vx_inertial = 0, vy_inertial = 0;\n  let x_rotating = 0, y_rotating = 0;  // Position in rotating frame\n  let vx_rotating = 0, vy_rotating = 0;\n  let theta = 0;  // Rotation angle\n  let time = 0;\n  \n  // Trail storage\n  const trail_inertial = [];\n  const trail_rotating = [];\n  \n  function glowDot(x,y,r,color,a){\n    const g=ctx.createRadialGradient(x,y,0,x,y,r*2.6);\n    const rgb=color.match(/\\d+/g);\n    g.addColorStop(0,'rgba('+rgb[0]+','+rgb[1]+','+rgb[2]+','+a+')');\n    g.addColorStop(1,'rgba('+rgb[0]+','+rgb[1]+','+rgb[2]+',0)');\n    ctx.fillStyle=g;ctx.beginPath();ctx.arc(x,y,r*2.6,0,Math.PI*2);ctx.fill();\n  }\n  \n  function trail(points,color){\n    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cy, 3, 0, Math.PI*2);ctx.fill();\n    \n    // Draw object\n    let px_draw = px + pw*0.15 + x_inertial * (pw*0.25);\n    let py_draw = py + ph*0.6 - y_inertial * (ph*0.25);\n    \n    if(is_rotating){\n      // Transform to rotating frame for display\n      const cos_t = Math.cos(theta);\n      const sin_t = Math.sin(theta);\n      const rx = x_rotating * cos_t - y_rotating * sin_t;\n      const ry = x_rotating * sin_t + y_rotating * cos_t;\n      px_draw = px + pw*0.15 + rx * (pw*0.25);\n      py_draw = py + ph*0.6 - ry * (ph*0.25);\n    }\n    \n    // Draw particle with glow\n    glowDot(px_draw, py_draw, 5, '99,200,255', 0.5);\n    ctx.fillStyle='#63b3ff';ctx.beginPath();ctx.arc(px_draw, py_draw, 4, 0, Math.PI*2);ctx.fill();\n    \n    // Draw velocity vector\n    const vel_scale = pw*0.08;\n    if(is_rotating){\n      const vmag = Math.sqrt(vx_rotating*vx_rotating + vy_rotating*vy_rotating);\n      if(vmag > 0.01){\n        arrow(px_draw, py_draw, px_draw + vx_rotating*vel_scale, py_draw - vy_rotating*vel_scale, '#87e8a8');\n      }\n    } else {\n      const vmag = Math.sqrt(vx_inertial*vx_inertial + vy_inertial*vy_inertial);\n      if(vmag > 0.01){\n        arrow(px_draw, py_draw, px_draw + vx_inertial*vel_scale, py_draw - vy_inertial*vel_scale, '#87e8a8');\n      }\n    }\n  }\n  \n  function tick(ts){\n    const dt=Math.min(0.016,(ts-lastTs)/1000);lastTs=ts;\n    const W=cv.width,H=cv.height;\n    \n    // Read sliders\n    const omega = Number(document.getElementById('c-omega').value);\n    const F_applied = Number(document.getElementById('c-force').value);\n    const mass = Number(document.getElementById('c-mass').value);\n    \n    // Update rotation angle\n    theta += omega * dt;\n    time += dt;\n    \n    // === INERTIAL FRAME (Stationary) ===\n    // Applied force is radial outward for simplicity\n    const F_x = F_applied * Math.cos(time * 2);\n    const F_y = F_applied * Math.sin(time * 2);\n    \n    // Acceleration in inertial frame: F = ma\n    const a_x = F_x / mass;\n    const a_y = F_y / mass;\n    \n    // Update velocity and position\n    vx_inertial += a_x * dt;\n    vy_inertial += a_y * dt;\n    x_inertial += vx_inertial * dt;\n    y_inertial += vy_inertial * dt;\n    \n    // Damping to keep in view\n    x_inertial *= 0.98;\n    y_inertial *= 0.98;\n    vx_inertial *= 0.98;\n    vy_inertial *= 0.98;\n    \n    // === ROTATING FRAME ===\n    // Transform inertial position to rotating frame\n    const cos_t = Math.cos(theta);\n    const sin_t = Math.sin(theta);\n    x_rotating = x_inertial * cos_t + y_inertial * sin_t;\n    y_rotating = -x_inertial * sin_t + y_inertial * cos_t;\n    \n    // Transform velocities\n    vx_rotating = vx_inertial * cos_t + vy_inertial * sin_t - omega * y_inertial;\n    vy_rotating = -vx_inertial * sin_t + vy_inertial * cos_t + omega * x_inertial;\n    \n    // Store trails\n    const trail_max = 80;\n    trail_inertial.push({x: x_inertial, y: y_inertial});\n    if(trail_inertial.length > trail_max) trail_inertial.shift();\n    \n    trail_rotating.push({x: x_rotating, y: y_rotating});\n    if(trail_rotating.length > trail_max) trail_rotating.shift();\n    \n    // === DRAW ===\n    ctx.clearRect(0,0,","remediationGoal":"Close wrong_assumption for physics."},"rendererStyle":"three_js"},"simulation_title":"Pseudo Force in Non-Inertial Frames"}},"metadata":{"rendered_at":"2026-05-13T20:41:08.705Z","cache_hit":false,"cost_usd":0},"error":null}