Dynamics extends statics by considering bodies in motion and the forces that cause that motion. The foundation is built on Newton's three laws of motion. The first law states that a body remains at rest or in uniform motion unless acted upon by a net external force. The second law relates the net force to mass and acceleration through \(F = ma\). The third law asserts that for every action there is an equal and opposite reaction, \(F_{12} = -F_{21}\).
Two important theorems follow from Newton's laws. The work-energy theorem states that the net work done on a body equals its change in kinetic energy, \(W_{net} = \Delta KE = \tfrac{1}{2}mv_2^2 - \tfrac{1}{2}mv_1^2\). The impulse-momentum theorem states that the impulse (force multiplied by time) equals the change in momentum, \(F\Delta t = \Delta(mv)\), where linear momentum itself is defined as \(p = mv\). It is important to distinguish kinematics, which describes motion without regard to its causes, from kinetics, which relates forces to the resulting motion.
For rotational motion, angular velocity \(\omega = d\theta/dt\) is the rate of change of angular displacement, measured in rad/s. A body moving along a circular path experiences centripetal acceleration directed toward the center, given by \(a_c = v^2/r = \omega^2 r\). D'Alembert's principle provides a useful bridge between dynamics and statics: by introducing an inertial force equal to \(-ma\) into a dynamic system, the problem can be analyzed as if it were in static equilibrium.