Rotational KE and work

Derive equation KE = 1/2 Iω2 by considering the KE energy of individual particles of a rigid body.Derive W = Γθ by considering the work done by small displacments of a rotating force.Calculate the KE gained when a torque is applied to a rigid body.Understand why a rolling ball gets down a slope slower than a sliding one.Derive the equation for the final velocity of a ball rolling down a slope.

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