Classical mechanics

Kinematics is the description of motion. In one dimension with constant acceleration a, the velocity changes linearly with time and the position is a quadratic. These formulas are integrals of a = constant, nothing more. The sign of a is part of the answer: acceleration opposite the velocity is slowing down, even if the number you were given was written as a positive “deceleration.”

Newton’s first law is the statement that a frame with no acceleration exists, and in it a body with no net force moves at constant velocity. The second law, F_net = ma, defines how the net force changes the motion. The third says forces come in pairs: the force of A on B is equal and opposite the force of B on A, and those two forces act on different bodies, so they do not cancel inside a single free-body diagram. Weight near Earth is mg, with g about 9.81 m/s² downward. The normal force is whatever a surface must push to enforce the constraint; it is not automatically mg.

Momentum p = mv is the quantity whose rate of change is the net force. In an isolated system the total momentum is constant, which is how you solve collisions without knowing the messy forces during the crash. Kinetic energy is not similarly conserved in an inelastic collision. Uniform circular motion keeps the speed constant while the direction changes, so there is an acceleration v²/r toward the center, and therefore a net force mv²/r toward the center. That force is not a new kind of force. It is friction, tension, gravity, or some other real force, required to point inward.