Kinetics

Kinematics tells us how a body moves; kinetics tells us why. Newton’s second law connects the net force acting on a body to its acceleration, transforming the equilibrium analysis of statics into the differential equations of dynamics. The free body diagram remains the central modelling tool, but now the sum of forces equals mass times acceleration rather than zero, and the solution is a trajectory rather than a set of reaction forces.

We begin with particle kinetics, where a body translates under the action of forces but does not rotate. The workflow mirrors statics closely: draw the free body diagram, write the equations of motion, specify initial conditions, and solve the resulting ordinary differential equations. The difference is that the solution describes how position, velocity and forces evolve over time. We treat both transient problems, solved by integrating the equations of motion forward in time, and energy methods, which relate changes in speed to work done without requiring the full time history.

Rigid body kinetics extends the framework to bodies that rotate as well as translate. The moment of inertia and its practical companion, the radius of gyration, characterize how mass is distributed relative to an axis of rotation. These quantities determine a body’s resistance to angular acceleration in the same way that mass determines its resistance to linear acceleration. Together, the translational and rotational equations of motion form the complete description of how forces and moments drive the motion of real mechanical systems.