Basic Assumptions of Classical Mechanics


A body consists of several particles. Each particle can be subdivided into molecules, atoms and electrons etc. It is not feasible to solve an engineering problem by treating a body as a conglomeration of such discrete particles. The body is assumed to consist of a continuous distribution of matter. In other words, body is treated as continuum.

The mass density  at a point P is a continuum is defined as the ratio of the mass element to the volume element ΔV enclosing the point , in the limit when  tends to zero.


Note that, here the assumption is that mass is the continuous function of the volume. In the right picture of Fig.1, mass is not a continuous function of volume. In the limit, one may end up in a void.


Fig.1: Concept of continuum

This course will act as a foundation for fluid mechanics and solid mechanics courses. There, we deal with deformable bodies. In this course, we will be studying the behavior of rigid bodies under forces.

Rigid body

A body is considered rigid when the changes in distance between any two of its points is negligible for the purpose at end or, A rigid body is a body that does not deform under the action of forces.

Deformable body:

A body is considered deformable when the changes in distance between any two of its points cannot be neglected.

Above mentioned assumptions are called Basic Assumptions of Classical Mechanics.

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