Physics
Conical pendulum
A bob swept round a cone: tension leans in, its horizontal part is the centripetal force, and only one spin rate holds the angle steady.
What happens
Spin a pendulum sideways and it sweeps a cone. The string tension leans inwards; its vertical part carries the weight and its horizontal part bends the path into a circle. Only one angular speed holds a given angle - detune it and the bob nods up and down as it goes round, because what is really being solved here is the full spherical pendulum, not the cone.
Equations used in the module
Equations θ'' = φ'² sin θ cos θ − (g/L) sin θ sin²θ φ' = const T = m[g cos θ + L(θ'² + φ'² sin²θ)] θ' = θ'' = 0: cos θ = g/(Lω²), T = mLω², P = 2π/ω ω ≤ √(g/L): θ = 0, T = mg
