Mechanics & Dynamics
Mechanics is the study of how interactions change motion. Specify the forces on a system and you can, in principle, predict its entire future — where it goes, how fast, and when.
Kinematics comes first — position, velocity, and acceleration as the geometry of motion, before any mention of what causes it. Vectors carry that geometry into two and three dimensions.
Then Newton's laws supply the cause. Force equals mass times acceleration is a differential equation for the trajectory, and the art is learning to read the forces off a situation and write it down.
Solving the equations directly is often hard, so mechanics leans on conservation laws. Energy is the first: work done on a body changes its kinetic energy, and stored potential energy converts back into motion.
Momentum is the second, and it makes collisions and many-body problems tractable. Whatever the internal forces, the total momentum of an isolated system is unchanged.
Extend the same ideas to spinning bodies and you get rotational inertia, torque, and angular momentum — the conserved quantity behind everything from a spinning top to a planet's orbit.
Gravitation ties it together. One inverse-square law explains falling apples and planetary orbits alike, and Kepler's empirical rules fall out of Newton's mechanics as a consequence.
From there the same framework reaches static equilibrium, fluids at rest and in flow, oscillations and travelling waves, and the thermal behaviour of matter — one language for the mechanical world.