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## Homework Statement

Find the Lagrangian of a simple pendulum of mass m whose point of support moves uniformly on a vertical circle with constant angular velocity.

(So basically there is a circle around the origin that spins with a constant angular velocity and the pendulum is attached to the end of the circle.)

## Homework Equations

[tex]\frac{d}{dt}\frac{∂L}{∂ \dot{q}_k}=\frac{∂L}{∂q_k}[/tex]

## The Attempt at a Solution

I am stuck right in the beginning in trying to find the kinetic energy T. I know that the kinetic energy of a pendulum is..

[tex]T=\frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2)[/tex]

But since r remains constant on the pendulum because it is rigid, the equation reduces to..

[tex]T=\frac{1}{2}mr^2\dot{\theta}^2[/tex]

I am unsure how to add the rotating circle in which the pendulum is a attached to. If the problem stated that there was a mass where the pendulum was attached to, it would be easier I think. Should I view this circle as mass-less? How would I get the kinetic energy then? Can anyone provide some help?? :(??