A "Cycloid" curve is one for which all objects take the 𝑠𝑎𝑚𝑒 amount of time to reach the bottom • If this seems counterintuitive, remember that 𝑚𝑔ℎ=½𝑚𝑣², and so objects starting higher will have a larger final velocitypic.twitter.com/EV4ZzT6YFo
-
-
Prikaži ovu nit
-
A Cycloid curve is also called a "Tautochrone" (meaning equal time) Mathematically, the Brachistochrone and the Cycloid are the same curve, but they arise from slightly different but related problems (equal time & least time) Brachistochrone ⇔ Cycloid Tautochrone ⇔ Cycloid
Prikaži ovu nit -
We learn in high school that the "period of a pendulum is independent of its amplitude"--i.e that it's isochronus. • This isn't quite true; it's only true for *small* angles θ • In reality, a pendulum's period is only independent of its amplitude if it moves along a cycloidpic.twitter.com/d1Vh1VlJ9u
Prikaži ovu nit -
gif credits: Brachistochrone: Robert Ferréol (Wikipedia) Tautochrone: Claudio Rocchini (Wikipedia) Pendulum : Rem088roy (Wikipedia)
Prikaži ovu nit -
A Cycloid is the curve traced out by a point on a rolling wheelpic.twitter.com/3BgmeSPDQF
Prikaži ovu nit -
gif credit: Cycloid rolling (last gif): IchibanPL (Wikipedia)
Prikaži ovu nit
Kraj razgovora
Novi razgovor -
-
-
Really interesting post. Makes me wonder what the lines would look like if the objects were moving closer to the speed of light, if that would change anything.
-
that is an interesting question
- Još 13 drugih odgovora
Novi razgovor -
-
-
Only applies if gravity (and acceleration) in play, right? Rolling balls along grooves on a table, for example, now the line is fastest again
-
yes.. but there’s nothing special about g=9.8m/s^2.. it’s the fact that it’s (1) downward and (2) constant
- Još 2 druga odgovora
Novi razgovor -
Čini se da učitavanje traje već neko vrijeme.
Twitter je možda preopterećen ili ima kratkotrajnih poteškoća u radu. Pokušajte ponovno ili potražite dodatne informacije u odjeljku Status Twittera.