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Physics

Ball on a spinning arm

A heavy ball on a rope from a rotating arm: it lags the arm and swings outward by inertia; cut the motor and the orbit spirals back in.

Ball on a spinning arm — Actual application image
Actual application image

What happens

A heavy ball on a rope from a rotating arm: it lags the arm and swings outward by inertia; cut the motor and the orbit spirals back in. The massless rope can pull but cannot push. A slack rope permits free flight; motor speed is prescribed.

Equations used in the module
Equations
P = (R cos φ, 0, R sin φ); φ' = Ω
Ω' = (Ω_target−Ω)/τ
m x'' = mg − c x' − T n
|x−P| ≤ L; T ≥ 0; T(L−|x−P|) = 0
|x−P| < L: T = 0

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