The kinetic energy of a rotating bar can be calculated using the moment of inertia and angular velocity. If the bar has varying speeds along its mass, calculus may be necessary to determine the moment of inertia accurately. The formula for rotational energy is given as 1/2 I ω², where I is the moment of inertia and ω is the angular velocity. Understanding these concepts is essential for calculating the kinetic energy in such scenarios. Accurate calculations depend on the specific distribution of mass and the axis of rotation.