Kinetic energy is equal to 1/2 mv2, where m is the mass and v2 is the velocity squared.
Since velocity is squared and mass isn't, it is velocity that is of greater importance.
The whipping action of a belt, and the ability to follow through with a swing, results is a velocity that is greater than what the arm can provide in a spank. Furthermore, the kinetic energy is applied to a smaller area on a belt than with the hand.
How about a pencil?
I’m glad someone could explain why the belt hurt more than dad’s hand.