(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A physical pendulum is made of a cord of length S with no mass and a bar attached to the cord, of length L and mass m.

We apart it from the vertical with an angle of [tex]\theta[/tex] °. We then release it.

1)Find the center of mass' velocity of the pendulum when it reaches the vertical position.

2)If the cord break up just after passing by the vertical position, find the angular velocity of the bar.

2. The attempt at a solution

I don't really know how to approach the problem (I'll try to do alone part b). I thought about conservation of energy but I have too many unknowns ([tex]v_{cm_{\text{initial}}}[/tex], [tex]\omega_{\text{final}}[/tex] and [tex]\omega_{\text{final}}[/tex]).

By the way I've calculated the moment of inertia of the pendulum as being worth [tex]m\left ( \frac{L^2}{3}+SL+S^2 \right )[/tex] because I'm sure I'll have to use it.

Should I write down the solution of the differential equation of motion of the pendulum?

[tex]\frac{d^2 \theta}{dt^2}=\omega ^2 \theta[/tex] where [tex]\omega=\sqrt{\frac{mg(S+L/2)}{I}}[/tex] is the diff. eq. of the motion and the solution is [tex]\theta (t)= \theta _A \cos (\omega t +\phi)[/tex]...

A little help is appreciated.

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# Homework Help: Physical pendulum problem

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