# Spring Angular Momentum Problem

1. Jan 19, 2015

### Rmehtany

1. The problem statement, all variables and given/known data

2. Relevant equations
PE spring = .5 kx^2
KE rotation = .5 I w^2

3. The attempt at a solution
I tried to do a conservation of energy
(Note: I = moment of inertia, L = length)
3*.5*k L^2 = .5 I w^2

I =3 M R^2 ---> a^2 = b^2 + c^2 -2bc cos(a) (the reason why I am using law of cosines is to find the radius from the center to each point mass)

R = L / sqrt(3)

I = ML^2

3*.5*k*L^2 = .5*M*L^2 *w^2

k = 1/3 * Mw^2 which is wrong. The answer is C. How do you do this?

2. Jan 19, 2015

### Quantum Defect

This is an equilibrium problem. The effective restoring force of the springs, acting on the masses, provides the centripetal force.

3. Jan 19, 2015

### Rmehtany

I see, Let me try. So the mass is 3m, and the Radius is calculated by law of cosines to be 4L/rad(3). so:

3*k*cos(30)* L = m*w^2 * 4L/rad(3)
k = m*w^2 * 2/9

I'm still messing up. What am I doing?

4. Jan 19, 2015

### Quantum Defect

Draw a vector diagram for the forces acting on one of the balls.

5. Jan 19, 2015

### Rmehtany

6. Jan 19, 2015

### Quantum Defect

Set the net inward force provided by the springs equal to the centripetal force, to maintain uniform circular motion.

7. Jan 19, 2015

### Rmehtany

OK

2 * f spring* cos(30) = f centripetal = rad(3) * f spring