The Spinning Chain Paradox · AI Generator #GEN-FA5B431B
Physics · mechanics
Problem
A uniform chain of length L and mass M is arranged in a perfect circle on a frictionless horizontal table. The chain is given an initial angular velocity ω0 such that it rotates as a rigid body about its center. However, the chain is not rigidly connected - each infinitesimal segment can slide freely relative to its neighbors.
(a) Find the tension T(t) in the chain as a function of time.
(b) Determine the radius R(t) of the circular chain as a function of time.
(c) Calculate the time tf at which the chain's radius becomes infinite (i.e., when the chain breaks apart).
Given: The chain maintains its circular shape throughout the motion, and the initial radius is R0=2πL.