All Problems

The Fundamental Equation of Dynamics

Problem 1.92

A chain of mass mm forming a circle of radius RR is slipped on a smooth round cone with half-angle θ.\theta . Find the tension of the chain if it rotates with a constant angular velocity ω\omega about a vertical axis coinciding with the symmetry axis of the cone.

Reveal Answer
T=(cotθ+ω2R/g)mg/2πT=\left(\cot \theta+\omega^{2} R / g\right) m g / 2 \pi