Find the angular speed of a cylinder with a spring

1. Jun 29, 2012

Hernaner28

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

A cylinder of radious r=10cm and mass m=1Kg is attached to a spring of constant k=18N/m.
In every moment the cylinder rolls without slipping over the inclined plane with an angle of 30º.
The other extreme of the spring is attached to a fixed point O, as shown. If the cylinder is released from rest being the center of mass a distance L=43cm from point O, ¿which will be the angular speed of the cylinder when its center reaches a distance of L/2 from O?

2. Relevant equations

3. The attempt at a solution

I tried with conservation of energy:

$$\displaystyle {{E}_{0}}=\frac{1}{2}k{{L}^{2}}$$

$$\displaystyle {{E}_{f}}=\frac{1}{2}I\omega +\frac{1}{2}k\frac{{{L}^{2}}}{4}+mg\left( \frac{L}{2}\sin 30{}^\text{o} \right)+\frac{1}{2}m{{v}^{2}}$$

I have two unknown quantities the angular and linear speed.

But the angular and linear aceleration are not constant! So how can I figure out the value of V just at point L/2?

UPDATE: So stupid I am, v=wR and now I do get:

Thanks

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Last edited: Jun 29, 2012