In classical physics, linear and angular motion as well as linear and angular momentum have long been defined. In this paper it becomes apparent through analysis that there is much need for the presence and denotation for a new type of motion. As such, centrial motion is introduced and described as another form of motion not previously presented. Furthermore, a new form of momentum called centrial momentum is defined and elaborated. As a result, the motion of complex bodies can be analyzed and studied with much more simplicity and ease than previously done via classical physics. Along with the discussion of centrial motion and momentum, the concepts of linear motion based on the motion of momentum is also studied and analyzed and the law of motion of momentum is defined. Additionally, complex scenarios are introduced where the discussions assist in the much simpler understanding of the classical scenarios of the motions presented. It becomes readily apparent that the use of centrial motion equations and relationships derived are the best suited for the purposes of the study of these types of motions.In addition, in this paper, motion scenarios that cannot be explained by classical physics are discussed and adequately explained by presenting new concepts. Through deeper analyses, it is found that momentum is not conserved. However, the kinetic energy of an isolated system, if not transformed to other forms of energy, remains conserved.