Rolling/non-rolling motion of unsymmetrical bodies

  • #1
I have a sphere (mass m, radius r) whose centre of mass is r/2 distance away from its geometric centre. If it is kept on a smooth horizontal surface with the centre of mass at the same horizontal level as the geometric centre, what exactly is going to happen?

Also, I need to find out the velocity of the COM as the sphere turns by an angle (say, theta).

Given the the moment of inertia of the sphere about an axis passing through its COM and perpendicular to the plane of motion is mr2/3.

It's very tricky to me when it's NOT given that the sphere rolls without sliding (most problems related to unsymmetrical bodies have this mentioned).
 

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