solution:

If the boulder is moving without slipping with a linear velocity of 4.0m/s, then it must be true that the rim of the circle is moving with the same velocity. Consider if the boulder makes one complete rotation. The point that touches the ground comes back to touching the ground after the revolution, and it has gone one circumferance in length, the same translational distance that the center of mass has made.
Sum the rotational and the translational kinetic energies to find the total kinetic energy.

eqnarray9

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