# Help with spring rotating around its axis of rotational symm

1. Nov 6, 2015

### starlord37

1. The problem statement, all variables and given/known data
An astronaut on a spacewalk loses her grip on a circular garter spring (pictured below). Looking at the spring she notices that it is rotating around its axis of rotational symmetry at a rate of 300 rpm. The circumference of the rotating garter spring is 1% longer than that of the garter spring when at rest. Calculate the spring constant of the spring if the radius of the rotating garter spring is R = 20 cm and its mass is 1 kg. (We are looking for the spring constant of the spring if it were cut open and stretched along a straight line.)

2. Relevant equations
T= Ia T=dL/dt K=1/2Iw^2 PE=1/2kx^2

3. The attempt at a solution
I tried using energy but then realized I had no initial state to compare it to. Then I tried using forces and torque but got stuck. This problem is problem 2 from the Canadian Physics Olympiad
http://phas-outreach.sites.olt.ubc.ca/files/2015/08/CAP-en-v7.pdf

2. Nov 7, 2015

### Simon Bridge

Welcome to PF.
Did you reason it out? What is the physics at play here?

3. Nov 7, 2015

### starlord37

Thanks. Well I figured since it's being stretched, the restoring force of the spring might be why it's rotating. It has some rotational kinetic energy, and we can find that because we're given omega. It also has some spring potential energy. There's a force radially inward with magnitude mv^2/R. And there's a force from the spring in some direction. I think that's all the physics that's going on.

4. Nov 8, 2015

### Simon Bridge

OK. You have things a little garbled. Consider:
Where does the radially inwards force (the mv^2/r one) come from?
(Aside: is this the rightbequation? I.e what is m in this equation?)
How does stretching a spring cause it to rotate?

You are looking for a narrative like: as the spring spins faster, it's circumference gets ________ until .... (fill in the blanks.)

Once you understand the physics, you can write it out using maths.
If the unstretched circumference is C, then the stretched circumference is what?
What is the formula relating tension T in the spring to the change in circumference $\Delta C$