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## Homework Statement

I need to find equations of motion of system on picture. It is easy when one finds Lagrangian so I am not asking you to calculate it, but I'm not sure if I correctly calculated the kinetic energy, so If anyone can verify, I would be greatfull.

The rod has mass m, length 2a, and sphere has mass M, and radius a.

## The Attempt at a Solution

The rod:

[tex]E_{rod}=\frac{1}{2}mv_{CM_{rod}}+\frac{1}{2}I_{rod}\dot{\theta}^2[/tex]

Where I took [tex]I[/tex] of rod to be [tex]\frac{1}{3}m(2a)^2[/tex], over the edge of rod, not [tex]\frac{1}{12}m(2a)^2[/tex], inertia over center of mass of rod.

The same goes for the sphere:

[tex]E_{sphere}=\frac{1}{2}Mv_{CM_{sphere}}+\frac{1}{2}I_{sphere}\dot{\varphi}^2[/tex]

Where I took moment of intertia over point of connection of rod and sphere. [tex]I_{sphere}=I_{CM_{sphere}}+Ma^2[/tex].

Is this correct, or did I missed something?