(adsbygoogle = window.adsbygoogle || []).push({}); 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?

The correct answer is 5,1 rad/s.

2. Relevant equations

3. The attempt at a solution

I tried with conservation of energy:

[tex] \displaystyle {{E}_{0}}=\frac{1}{2}k{{L}^{2}}[/tex]

[tex] \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}}[/tex]

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:

w = 5.093459858 rad/s :)

Thanks

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# Homework Help: Find the angular speed of a cylinder with a spring

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