What is the long definition of rotational motion? What are the other types of motion?

There are broadly(in newtonian physics) 3 types of motions 1. rectilinear/translational motion 2. rotation( that i will shortly answer) 3. rolling(rectillinear +rotation combo.wow)

Imagine an axis passing through or anywhere near a body/mass/(say an axis passing perpendicular to plane of the disc). imagine it attached solidly to that body by itself or some imaginary glue. rotate that axis, sow ill the body rotate with it. So we say body is undergoing rotational motion. Defn:-if each particle of the "rigid" mass undergoes a about the same axis, and have same angular speed, the body is said to be undergoing ROTATIONAL MOTION.

There is no in relativity. since there is no "rogid" body concept there.

Hope it helps