Mechanics · Interactive

Ball on a String — Vertical Circle

A ball on a string is pushed sideways from the bottom. Gravity and string tension together bend its path into a circle — but only if it's fast enough. Too slow and the string goes slack near the top, letting the ball fall inward as a free projectile until the string snaps taut again.

→ Velocity → Tension Vertical plane · pushed from the bottom

Setup

Launch speed v₀ 7.0 m/s
String length L 1.20 m
Completes the loop
Motion regime
7.7
v₀ to loop (m/s)
—
v at top (m/s)
loop needs v₀² ≥ 5gL

Playback

Try this: sit just below the loop speed and watch the string go slack past the sides — the ball cuts across the circle as a projectile (the red tension arrow vanishes) before the string catches it. Drop lower still and it settles into a back-and-forth pendulum swing.