Some applications of the formulation developed in the last chapter for particle dynamics are discussed in this chapter. The motion of a particle near the surface of the Earth is first described, which can be used to explain some phenomena such as the Foucault pendulum and the hurricanes. After that, the familiar motion of a spherical pendulum is considered, for which the elliptic functions are used to find the closed-form solutions. The projectile problem and the motion of a particle in a central force field are discussed next, in which the notion of scattering angle in atomic physics is introduced. The many-body problem and the satellite’s motion in Earth’s orbit are also considered which finds various applications in satellite design. For systems of variable masses, the propulsion problem is studied first, followed by the motion of an electron with mass being related to its speed. From these applications, it is seen that the analysis of the equations of motion derived from Newton’s law may be rather involved.