# Fast question about Lagrangian

I've seen some problems solved in a weird way, I just want to be sure: the whole kinetic energy has to be in the lagrangian, right? For example, if we have a particle fixed in a plane with spherical coordinates $(r,\theta,\phi)=(r_0,\theta_0,\phi)$, and that plane is rotating with a constant angular velocity $\omega=(0,0,\omega_0)$, so that the $\phi$ coordinate of the particle is $\phi=\omega t$, then that term of the kinetic energy: in spherical coordinates: $\frac{1}{2}mr^2\omega^2\sin^2(\theta)$, that term has to go in the lagrangian, am I right? And does it have to go in the expression of the total mechanical energy?

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Could you clarify what exactly is rotating - the particle or the plane? How is the angle $\theta$ defined? –  Joe Jan 27 '13 at 19:25
@Joe I edited it to try to explain it better. –  MyUserIsThis Jan 27 '13 at 19:29