{"product_id":"the-heavy-top-plate-002-physics-poster","title":"The Heavy Top – Plate 002 Physics Poster","description":"\u003cp\u003ePlate 2 speaks for itself: \u003cem\u003e“Pulled down. Answers sideways.”\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eA symmetric top spinning with one point fixed feels gravity as a torque that turns its axis sideways (precession) with a small nodding (nutation). In Euler angles the Lagrangian contains neither φ nor ψ, so the matching momenta are conserved.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eL = (I₁\/2)(θ̇² + φ̇² sin²θ) + (I₃\/2)(ψ̇ + φ̇ cos θ)² − Mgℓ cos θ\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eL: Lagrangian, J\u003c\/li\u003e\n\u003cli\u003eI₁, I₃: moments of inertia about a transverse axis through the fixed point and about the symmetry axis, kg m²\u003c\/li\u003e\n\u003cli\u003eθ, φ, ψ: Euler angles: tilt, precession, spin, rad\u003c\/li\u003e\n\u003cli\u003eM: mass, kg\u003c\/li\u003e\n\u003cli\u003eg: gravitational acceleration, m s⁻²\u003c\/li\u003e\n\u003cli\u003eℓ: distance from fixed point to centre of mass, m\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eφ and ψ do not appear, so p_φ and p_ψ (kg m² s⁻¹) are conserved.\u003c\/p\u003e\u003ch3\u003eSources\u003c\/h3\u003e\u003cul\u003e\u003cli\u003eH. Goldstein, C. Poole, J. Safko, Classical Mechanics, 3rd ed., §5.7.\u003c\/li\u003e\u003c\/ul\u003e\u003ch3\u003eOn the poster\u003c\/h3\u003e\u003cp\u003ePlate 002, “The Heavy Top”: the pixel-art plate with its slogan “Pulled down. Answers sideways.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"9'' x 12\" (Vertical) \/ Matte","offer_id":50961402560615,"sku":"28624364330452609292","price":19.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Fine Art","offer_id":50961402593383,"sku":"20316290092811985313","price":29.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Semi Glossy","offer_id":50961402626151,"sku":"31166581556906756132","price":19.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Fine Art","offer_id":50961402658919,"sku":"17274568760827431550","price":44.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Semi Glossy","offer_id":50961402691687,"sku":"29547881498228384591","price":29.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Matte","offer_id":50961402724455,"sku":"22082129554404614797","price":29.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Matte","offer_id":50961402757223,"sku":"76821190225953990388","price":69.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Fine Art","offer_id":50961402789991,"sku":"11731576028909682689","price":119.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Semi Glossy","offer_id":50961402822759,"sku":"19768886299511741948","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/2899628060738354508_2048.jpg?v=1793631767","url":"https:\/\/pixelatedphysics.com\/fr\/products\/the-heavy-top-plate-002-physics-poster","provider":"Pixelated Physics","version":"1.0","type":"link"}