Why are radians cancelled from the kinetic energy of rotational motion, kg meters2 x radians2 / seconds2
Radians don't cancel because they were never there in the first place! Radians are dimensionless.
One radian is defined to be a angle such that the length of the arc subtended by that angle is equal to the radius of the circle. Since the angle in radians is determined by the ratio of the length of the arc divided by the radius of the circle the units of length cancel out. Fo example suppose that the length of the arc is 45 cm while the radius of the circle is 15 cm. The resulting angle will be theta=45cm/15cm=3 or 3 radians! Radians has no units - we merely use the word radians for convenience to keep track of the fact that 3 is an angle. But actually it is just as correct to say that the angle is 3 rather than say it is 3 radians. Therefore, any time it is convenient it is quite acceptable to just drop the radian designation because it was never really there in the first place.