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This problem illustrates the two contributions to the kinetic energy of an extended object: rotational kinetic...

This problem illustrates the two contributions to the kinetic energy of an extended object: rotational kinetic energy and translational kinetic energy. You are to find the total kinetic energy Ktotal of a dumbbell of mass mwhen it is rotating with angular speed ? and its center of mass is moving translationally with speed v. (Figure 1) Denote the dumbbell's moment of inertia about its center of mass by Icm. Note that 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=mr2, but this fact will not be necessary for this problem.

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Moment of inertia is expressed as 1cm-mr Total moment of inertia of both the masses is given as, since each has the mass of m

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