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

I've got a rigid rod, length [itex]2a[/itex], held at an angle [itex]\alpha[/itex] above a smooth horizontal surface. Its end is in contact with the ground. My two generalized coordinates are [itex]x[/itex], the horizontal position of the center of the rod and [itex]\theta[/itex] the angle between the rod and the vertical.

I'm trying to find the kinetic energy of the rod. I'm not sure if I'm doing it right.

2. Relevant equations

3. The attempt at a solution

As of now, this is what I've done:

[tex]KE = \frac{1}{2}m\dot{x}^2 + \frac{1}{2}I\dot{\theta}^2 = \frac{1}{2}m\dot{x}^2 + \frac{1}{2}(\frac{1}{3}m(2a)^2)\dot{\theta}^2 = \frac{1}{2}m\dot{x}^2 + \frac{2}{3}ma^2\dot{\theta}^2[/tex]

Something doesn't seem right though, because I think that [itex]\dot{x}[/itex] should be zero. Carrying out the Lagrangian doesn't seem to show this.

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# Homework Help: Kinetic Energy of rod with lower end in contact with smooth surface

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