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"Consider the system consisting of a bead of mass m sliding on a smooth circular wire hoop of mass 2m and radius R in a vertical plane, and the vertical plane containing the hoop free to rotate about the vertical axis. Let φ denote the angle between the plane containing the hoop and a fixed horizontal direction.

(You may assume that the moment of inertia of the hoop about an axis which contains a diameter of the hoop is equal to mR^2.)"

I need to find the lagrangian for the above problem. I was thinking of using spherical coordinates with constant radius for the particle but because the hoop has mass I'm a little confused. Do i need to use the additional coordinate of the centre of mass of the hoop, or am I overthinking the problem?

user339718
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  • This might be better on physics.SE –  May 25 '16 at 16:39
  • A picture/sketch of the scenario is the place to start, and would be a sensible addition to your question statement. – Semiclassical May 25 '16 at 17:12
  • My only issue is when considering the potential of the hoop. If we take the origin of the system to be at the centre of the hoop then can we ignore the potential of the Hoop? – user339718 May 25 '16 at 19:17

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