3 days ago
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Posted On: November 2nd 2026, 01:51 pm
Ball and spring in a rotating pipe
A pipe turns in a vertical plane about its center, with a ball inside tied to the center by a spring; gravity pulls down. The ball may pass through the pivot: the spring’s length is |r|, so the potential has two wells with a hump of height frac12kL_0^2 between them, and the wells rock up and down as the pipe turns. In the frame of the pipe the ball feels the spring, the centrifugal push mω^2r, gravity, and a sideways Coriolis force carried by the pipe wall (the normal force). With gravity switched off, below the critical speed ω_c=√k/m the ball oscillates about r_eq=kL_0/(k-mω^2); above it the centrifugal push wins and the ball is flung to an end. Switch the pipe from driven to free and…
Formula: m r=mω^2r-k(|r|-L_0)sgnr-mgsinθ
Open it and play with the settings: https://www.dm.ufscar.br/profs/waldeck/en/art.html?item=pipe#sketches-2
@infinitymathart
#mathart #mathematics #generativeart #creativecoding math
A pipe turns in a vertical plane about its center, with a ball inside tied to the center by a spring; gravity pulls down. The ball may pass through the pivot: the spring’s length is |r|, so the potential has two wells with a hump of height frac12kL_0^2 between them, and the wells rock up and down as the pipe turns. In the frame of the pipe the ball feels the spring, the centrifugal push mω^2r, gravity, and a sideways Coriolis force carried by the pipe wall (the normal force). With gravity switched off, below the critical speed ω_c=√k/m the ball oscillates about r_eq=kL_0/(k-mω^2); above it the centrifugal push wins and the ball is flung to an end. Switch the pipe from driven to free and…
Formula: m r=mω^2r-k(|r|-L_0)sgnr-mgsinθ
Open it and play with the settings: https://www.dm.ufscar.br/profs/waldeck/en/art.html?item=pipe#sketches-2
@infinitymathart
#mathart #mathematics #generativeart #creativecoding math
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