After the preparatory work in the previous chapters we here will define forces and derive Newton’s equations of motion; their solution will provide the trajectory of a mass point in space and time. Examples for characteristic problems will be given and the explicit solutions derived in detail. It will turn out that instead of velocities or angular velocities it is more convenient to introduce momenta and angular momenta of particles since for closed systems—without external forces—the total momentum is a constant of motion. This also holds for the angular momentum if no external torque acts on the system. Next we will consider the connection between the work done by a force on a particle along its trajectory and the actual kinetic energy. In case of conservative forces we can introduce a potential energy \(U({{\vec { r}}})\) that allows to compute the actual force by its negative gradient. Then the energy of the system can be defined by the sum of kinetic and potential energy and – for closed systems—is found to be a conserved quantity, too.