Newtons law for moments sais that the sum of the moments of the forces acting on a body is equal to the moment of inertia of the body about the center of gravity times the angular acceleration of the body.
For a body that is not rotating, the angular acceleration is equal to zero, which means that the right side of Newtons equation goes to zero.
When a body is static there is NO motion. Quasi-static motion in this sense is when the body is in pure translation -- meaning it is moving but NOT rotating. The above simplification holds true for both cases.
