What makes a rotation different from a translation?
This is a really good question because it’s important to understand the differences in order to understand the physics. Translational motion (also called linear) is simply an increment of distance dS traveled over an increment of time dT. As dS is a straight line over this small increment, there is no angular momentum. That is, there is no rotation or revolution of the object with the linear motion. In which case, all the object’s kinetic energy is linear kinetic energy KE(l) = 1/2 mV^2; where V = dS/dT the translational (linear) velocity of the object with mass m. Further, all its momentum is linear momentum P = mV. Rotational motion (also called spin) is where the object travels an increment of angle dTheta over an increment of time dT. The angle Theta is measured from some starting point (usually at time T = 0) and wraps around the spin axis, which is something like the hub of a wheel. If Theta = 360 degrees and the shape of the spin is circular, we can write C = Theta * R = 360 * R
