What exactly is force in physics?

Answer 1

Force F is exactly the space derivative of Energy W, F= XW.

Energy W is the sum of a scalar energy S/Potential and Vector energy V.

This gives Force F= X(S + V) = X[S,V]

F = [d/dr,Del][S,V] = [dS/dr - Del.V, dV/dr + Del S + DelxV]

There are generally five forces:

scalar derivative dS/dr, Centripetal Force

Divergence Del.V , Centrifugal Force

Tangent dV/dr = dV/cdt, Tangent Force

Gradient Del S , Radial force

and Curl DelxV Circular Force.