Pendulum: Effect of Gravity

Period of a pendulum T = 2π√(L/g) — inversely proportional to √g.

Smaller g (higher altitude, equator, Moon) ⇒ LONGER period.

Higher g (poles, Earth's center) ⇒ SHORTER period.

Pendulums historically used to measure g — extremely precise at ~10⁻⁵.

Pendulum at top of mountain runs SLOW: g drops by ~0.3% at 10 km altitude.

Pendulum at equator runs slightly slower than at poles due to Earth's rotation + oblateness.

On the Moon (g ≈ 1.6 m/s²): T_moon ≈ 2.45 × T_earth.

g measurement: g = 4π²L/T². Modern atom-interferometer measurements: g to 10⁻⁹ precision.