The same two accounts, spinning
The translation table finishes here. Mass becomes moment of inertia ; speed becomes angular velocity ; and the two great bookkeeping quantities of mechanics come across unchanged in shape. Kinetic energy becomes — KE equals one-half I omega squared — where is in , is in , and the answer is in joules, the same joules as everywhere else.
Momentum becomes angular momentum — L equals I omega — in . No ½, no square: momentum never had either, and its rotational twin does not acquire them. Telling the two apart on an exam paper is a units question and nothing more. Joules means energy; means momentum.
The square in the energy is where flywheels earn their keep: double the speed and a wheel banks four times the energy, while its angular momentum merely doubles. That is why a modest steel disk spun fast can smooth a punch press through a stroke that would otherwise stall the motor — and why the same disk is a serious object to be standing beside when a bearing lets go.