{"job_id":"anim-job-3d644b41-9da6-4787-a61b-60fad0ebeb5f","request_id":"test-physics-newton-ba30c5e5-e5bb-4ff3-90a7-a40b2e480a51-1778708287067","status":"complete","asset":{"primary_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-3d644b41-9da6-4787-a61b-60fad0ebeb5f/walkthrough.mp4","thumbnail_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-3d644b41-9da6-4787-a61b-60fad0ebeb5f/thumb.jpg","transcript_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-3d644b41-9da6-4787-a61b-60fad0ebeb5f/transcript.vtt","interactive_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-3d644b41-9da6-4787-a61b-60fad0ebeb5f/index.html","scenefile_url":"https://storage.googleapis.com/pupiltree-animation-assets/anim-job-3d644b41-9da6-4787-a61b-60fad0ebeb5f/scene-source.json","duration_seconds":15,"byte_size":464952,"renderer":"html_three_js_local","parameters":{"style":"auto","executor":"native_render_executor","localPath":"/app/storage/assets/anim-job-3d644b41-9da6-4787-a61b-60fad0ebeb5f","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-3d644b41-9da6-4787-a61b-60fad0ebeb5f","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 Non-Inertial 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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id=\"v-radius\">2.0</strong></span><input id=\"c-radius\" type=\"range\" min=\"1\" max=\"4\" step=\"0.1\" value=\"2.0\"/></label>\n    <ul>\n      <li><span class=\"misconception\">✗</span> <strong>Wrong:</strong> Apply F=ma ignoring rotation</li>\n      <li><span class=\"correction\">✓</span> <strong>Correct:</strong> Add centrifugal pseudo force outward</li>\n      <li>In rotating frame: object needs radial force to stay at rest</li>\n      <li>Centrifugal: F_cf = mω²r (opposite frame acceleration)</li>\n    </ul>\n  </aside>\n  <section>\n    <div class=\"stage\" id=\"stage\">\n      <div class=\"legend\" id=\"legend\">Inertial view</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\":4,\"step\":0.1,\"value\":2.0,\"units\":\"rad/s\"},{\"key\":\"mass\",\"label\":\"Mass\",\"min\":0.5,\"max\":3,\"step\":0.1,\"value\":1.0,\"units\":\"kg\"},{\"key\":\"radius\",\"label\":\"Radius\",\"min\":1,\"max\":4,\"step\":0.1,\"value\":2.0,\"units\":\"m\"}];\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 time=0;\n  let angle=0;\n  let showWrong=true;\n  let toggleTime=0;\n  \n  // Trail for object motion\n  let trail=[];\n  const maxTrailLen=60;\n  \n  function glowDot(x,y,r,color,a){\n    const g=ctx.createRadialGradient(x,y,0,x,y,r*2.6);\n    g.addColorStop(0,color.replace('ALPHA',String(a)));\n    g.addColorStop(1,color.replace('ALPHA','0'));\n    ctx.fillStyle=g;ctx.beginPath();ctx.arc(x,y,r*2.6,0,Math.PI*2);ctx.fill();\n  }\n  \n  function drawArrow(x1,y1,x2,y2,color,w){\n    const dx=x2-x1,dy=y2-y1,l=Math.sqrt(dx*dx+dy*dy);\n    if(l<1)return;\n    const nx=dx/l,ny=dy/l,s=12;\n    ctx.strokeStyle=color;ctx.lineWidth=w||2;ctx.beginPath();ctx.moveTo(x1,y1);ctx.lineTo(x2,y2);ctx.stroke();\n    ctx.fillStyle=color;ctx.beginPath();ctx.moveTo(x2,y2);\n    ctx.lineTo(x2-s*nx+s*0.4*ny,y2-s*ny-s*0.4*nx);\n    ctx.lineTo(x2-s*nx-s*0.4*ny,y2-s*ny+s*0.4*nx);ctx.fill();\n  }\n  \n  function tick(ts){\n    const dt=Math.min(0.04,(ts-lastTs)/1000);lastTs=ts;\n    const W=cv.width,H=cv.height;\n    time+=dt;\n    \n    // Read sliders\n    const omega=parseFloat(document.getElementById('c-omega').value)||2.0;\n    const mass=parseFloat(document.getElementById('c-mass').value)||1.0;\n    const radius=parseFloat(document.getElementById('c-radius').value)||2.0;\n    \n    // Rotate angle\n    angle+=omega*dt;\n    \n    // Toggle between wrong and correct view every 7.5s\n    toggleTime+=dt;\n    if(toggleTime>15){toggleTime=0;}\n    showWrong=(toggleTime<7.5);\n    \n    // Position in inertial frame (circular motion)\n    const px=W/2 + radius*60*Math.cos(angle);\n    const py=H/2 + radius*60*Math.sin(angle);\n    \n    // Velocity (tangent to circle)\n    const vx=-radius*60*omega*Math.sin(angle);\n    const vy=radius*60*omega*Math.cos(angle);\n    \n    // Centripetal acceleration needed (pointing to center)\n    const a_cent=omega*omega*radius*60;\n    const a_cent_x=-a_cent*Math.cos(angle);\n    const a_cent_y=-a_cent*Math.sin(angle);\n    \n    // Add to trail\n    trail.push({x:px,y:py});\n    if(trail.length>maxTrailLen)trail.shift();\n    \n    // Clear canvas\n    ctx.fillStyle='#0f1418';ctx.fillRect(0,0,W,H);\n    \n    // Draw radial grid\n    ctx.strokeStyle='rgba(45, 62, 70, 0.3)';ctx.lineWidth=1;\n    for(let r=1;r<=5;r++){\n      ctx.beginPath();ctx.arc(W/2,H/2,r*50,0,Math.PI*2);ctx.stroke();\n    }\n    for(let a=0;a<Math.PI*2;a+=Math.PI/6){\n      ctx.beginPath();ctx.moveTo(W/2,H/2);\n      ctx.lineTo(W/2+280*Math.cos(a),H/2+280*Math.sin(a));\n      ctx.stroke();\n    }\n    \n    // Draw rotation axis (platform)\n    ctx.fillStyle='rgba(99, 179, 255, 0.15)';ctx.beginPath();ctx.arc(W/2,H/2,radius*60+40,0,Math.PI*2);ctx.fill();\n    ctx.strokeStyle='#445862';ctx.lineWidth=2;ctx.beginPath();ctx.arc(W/2,H/2,radius*60+40,0,Math.PI*2);ctx.stroke();\n    \n    // Draw object trail\n    if(trail.length>1){\n      ctx.strokeStyle='rgba(135, 232, 168, 0.3)';ctx.lineWidth=2;\n      ctx.beginPath();ctx.moveTo(trail[0].x,trail[0].y);\n      for(let i=1;i<trail.length;i++){\n        ctx.lineTo(trail[i].x,trail[i].y);\n      }\n      ctx.stroke();\n    }\n    \n    // Draw object\n    ctx.fillStyle='#63b3ff';glowDot(px,py,8,'rgba(99,179,255,ALPHA)',0.4);\n    ctx.fillStyle='#63b3ff';ctx.beginPath();ctx.arc(px,py,8,0,Math.PI*2);ctx.fillRect(px-5,py-5,10,10);\n    \n    // Draw velocity vector\n    const v_scale=0.8;\n    drawArrow(px,py,px+vx*v_scale,py+vy*v_scale,'#87e8a8',2.5);\n    \n    if(showWrong){\n      // WRONG view: ignore pseudo force\n      ctx.fillStyle='#de7f76';\n      ctx.font=Math.round(H*0.05)+'px sans-serif';\n      ctx.textAlign='left';\n      ctx.fillText('❌ WRONG: F=ma only (inertial)',20,40);\n      ctx.fillStyle='rgba(222, 127, 118, 0.6)';\n      ctx.font=Math.round(H*0.035)+'px sans-serif';\n      ctx.fillText('Ignoring rotation frame acceleration',20,70);\n      \n      // Draw only applied (centripetal) force\n      const f_applied_scale=0.15;\n      drawArrow(px,py,px+a_cent_x*f_applied_scale,py+a_cent_y*f_applied_scale,'#de7f76',3);\n      \n      ctx.fillStyle='#de7f76';ctx.font=Math.round(H*0.032)+'px sans-serif';\n      ctx.textAlign='center';\n      ctx.fillText('F_applied',px+a_cent_x*f_applied_scale*0.5-30,py+a_cent_y*f_applied_scale*0.5-15);\n      \n      // Show prediction (wrong trajectory)\n      ctx.strokeStyle='rgba(222, 127, 118, 0.35)';ctx.lineWidth=2;ctx.setLineDash([4,4]);\n      ctx.beginPath();ctx.arc(W/2,H/2,(radius-1)*60,0,Math.PI*2);ctx.stroke();\n      ctx.setLineDash([]);\n      \n      ctx.fillStyle='var(--red)';ctx.font=Math.round(H*0.04)+'px sans-serif';\n      ctx.textAlign='center';\n      ctx.fillText('Object spirals inward',W/2,H-40);\n      \n    } else {\n      // CORRECT view: include pseudo force\n      ctx.fillStyle='#87e8a8';\n      ctx.font=Math.round(H*0.05)+'px sans-serif';\n      ctx.textAlign='left';\n      ctx.fillText('✓ CORRECT: F + F_pseudo = ma\\'',20,40);\n      ctx.fillStyle='rgba(135, 232, 168, 0.6)';\n      ctx.font=Math.round(H*0.035)+'px sans-serif';\n      ctx.fillText('In rotating frame, add centrifugal force',20,70);\n      \n      // Draw centripetal force (toward center)\n      const f_cent_scale=0.15;\n      drawArrow(px,py,px+a_cent_x*f_cent_scale,py+a_cent_y*f_cent_scale,'#63b3ff',3);\n      ctx.fillStyle='#63b3ff';ctx.font=Math.round(H*0.032)+'px sans-serif';\n      ctx.textAlign='center';\n      ctx.fillText('F_centripetal',px+a_cent_x*f_cent_scale*0.5-35,py+a_cent_y*f_cent_scale*0.5-20);\n      \n      // Draw centrifugal pseudo force (outward)\n      const f_pseudo_scale=0.15;","remediationGoal":"Close wrong_assumption for physics."},"rendererStyle":"three_js"},"simulation_title":"Pseudo Force in Non-Inertial Frames"}},"metadata":{"rendered_at":"2026-05-13T21:43:09.463Z","cache_hit":false,"cost_usd":0},"error":null}