18 Apr '08 08:09

Suppose you have a closed loop of rope in the shape of a circle of radius 1m. It's floating in space, and rotating in the plane of the circle and about the center of the circle at 1 rad/s. This creates a "centrifugal force" which keeps the loop taut. What is the tension in the rope? Generalize to arbitrary radii and rotation speeds.

Equivalently, we may consider a loop made out of a "springy" material which obey's Hooke's law: suppose we have a loop of material with a rest length of 0m and a spring constant of 1 N/m; what is its equilibrium radius if it rotates as above? Generalize to arbitrary spring constants and rotation speeds.

I think this problem can be generalized to 3 dimensions like so: a beach ball of radius 1m floats in space; its internal air pressure is 1 Pa; what is the "tension" in the ball? The problem is giving a rigorous definition of the tension (or equivalently the spring constant) of 2d surface, which I don't know how to do.

Equivalently, we may consider a loop made out of a "springy" material which obey's Hooke's law: suppose we have a loop of material with a rest length of 0m and a spring constant of 1 N/m; what is its equilibrium radius if it rotates as above? Generalize to arbitrary spring constants and rotation speeds.

I think this problem can be generalized to 3 dimensions like so: a beach ball of radius 1m floats in space; its internal air pressure is 1 Pa; what is the "tension" in the ball? The problem is giving a rigorous definition of the tension (or equivalently the spring constant) of 2d surface, which I don't know how to do.