Find the total kinetic energy Ktot of a dumbbell of mass m when it is rotating with angular speed Ï and its center of mass is moving translationally with speed v. Denote the dumbbell's moment of inertia about its center of mass by Icm. Note: If you approximate the spheres as point masses of mass m/2 each located a distance r from the center and ignore the moment of inertia of the connecting rod, then the moment of inertia of the dumbbell is given by Icm=mr^2, but this fact will not be necessary for this problem. Required:
Find the total kinetic energy Ktot of the dumbell.

Explanation:

Total kinetic energy of dumbbell = translational kinetic energy + Rotational kinetic energy

Translational kinetic energy = 1/2 m v²

Rotational kinetic energy = 1/2 x moment of inertia about CM  x angular speed

= 1/2  x Icm x Ï ²

Total kinetic energy

Ktot = 1/2 m v² + 1/2  x Icm x Ï ²

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