Classical Mechanics

An object remains at rest or in a state of uniform motion in a straight line unless acted upon by a net external force.

The rate of change of momentum of a body is directly proportional to the applied force and occurs in the direction of the force; often expressed as $F = ma$ for constant mass.

For every action, there is an equal and opposite reaction.

Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers: $F = G \frac{m_1 m_2}{r^2}$.

The force needed to extend or compress a spring by some distance scales linearly with respect to that distance: $F = -kx$.

For any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as system mass cannot change, so quantity cannot be added nor removed.

In a closed system (one that does not exchange any matter with its surroundings and is not acted on by external forces), the total momentum is constant.

When the net external torque acting on a system about a given axis is zero, the total angular momentum of the system about that axis remains constant.

For a system of particles, the sum of the differences between the applied forces and the inertial forces is zero.

The dynamics of a physical system are determined by a variational problem for a functional based on a single function, the Lagrangian, which contains all physical information concerning the system and the forces acting on it.

The coefficient of restitution is the ratio of the final to initial relative velocity between two objects after they collide.