{"product_id":"cavenda-weighing-the-world-1798-physics-t-shirt","title":"Cavenda – Weighing the World 1798 Physics T-Shirt","description":"\u003cp\u003eCavenda peers through a telescope at a twitching dumbbell, with the whole Earth balanced on the other end of the beam.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eA torsion balance hangs a light arm with a small lead ball at each end. Large lead spheres brought close pull on the balls and twist the arm by a tiny angle; from that twist and the swing period you can work out the Earth's mean density. The gravity, twist and period relations below are the standard torsion-balance equations.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eF = G M m \/ r²,   κθ = F L,   T = 2π √(I \/ κ)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eF: gravitational force (N)\u003c\/li\u003e\n\u003cli\u003eG: gravitational constant (m³ kg⁻¹ s⁻²)\u003c\/li\u003e\n\u003cli\u003eM, m: large and small masses (kg)\u003c\/li\u003e\n\u003cli\u003er: centre-to-centre distance (m)\u003c\/li\u003e\n\u003cli\u003eκ: torsion constant (N·m\/rad)\u003c\/li\u003e\n\u003cli\u003eθ: twist angle (rad)\u003c\/li\u003e\n\u003cli\u003eL: lever arm (m)\u003c\/li\u003e\n\u003cli\u003eT: swing period (s)\u003c\/li\u003e\n\u003cli\u003eI: moment of inertia (kg·m²)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eHenry Cavendish's paper was read to the Royal Society on 21 June 1798, using a torsion balance devised by John Michell. He printed Earth's density as 5.48 times water; his own data give 5.448, and today's value is about 5.51.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e He reported Earth's density, not G. Today's G (CODATA 2022) is 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻².\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Cavenda, the pixel-art character, with the title. Back: the three torsion-balance equations, Earth's density then and now, today's G and the 1798 paper. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936682250343,"sku":"37795753849947355436","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936682283111,"sku":"13090683425263620724","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936682315879,"sku":"26289388106781649872","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936682348647,"sku":"12767194343473219221","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936682381415,"sku":"32342451147733937124","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936682414183,"sku":"13307789072658842258","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936682446951,"sku":"13082477554228574138","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936682479719,"sku":"16692024027180265100","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936682512487,"sku":"17866232577370615908","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936682545255,"sku":"16745689790209441435","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936682578023,"sku":"17605386382258146845","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936682610791,"sku":"72284303915766614462","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936682643559,"sku":"32482620619026896891","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936682676327,"sku":"10582135256456441440","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936682709095,"sku":"26086854514066238291","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936682741863,"sku":"19374001270203333237","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/cavendish-1798_front_01_white.png?v=1793595905","url":"https:\/\/pixelatedphysics.com\/hi\/products\/cavenda-weighing-the-world-1798-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}