5 ms·
If the length of a meter were defined as the length of a seconds pendulum [1], then g would equal exactly π². From the pendulum equation: `T = 2π√(L/g)` subst
by kaapipo 2y ago
If the length of a meter were defined as the length of a seconds pendulum [1], then g would equal exactly π². From the pendulum equation:
`T = 2π√(L/g)`
substitute T = 2 s and L = 1 m:
`2 s = 2π√(1 m / g)`
solve for g:
`g = π² m/s²`.
This holds up in any strength of gravity, but the length of a meter would be different depending on it.
[1]. This actually was proposed by Talleyrand in 1790. Imagine the world if this were true!
- n4r9 2y agoThe article explains that Huygens proposed this in the 17th C, and gives the same derivation :)