Idealizations

Idealizations

• Idealizations are used in mechanics to simplify practical problems without appreciable loss of accuracy. The following idealizations are frequently used in mechanics :

Particle :

• It is an object that has mass but no dimensions.

• In some practical situations in which there is only translational motion of objects, their dimensions are not required. For example, to study motion of earth around the sun, the dimensions of the earth are not important and it is treated like a particle. Its dimensions are required while studying its rotational motion about its axis.

• Note that a particle can have only translational motion. It cannot have rotational motion.

Rigid body:

• It can be considered as a combination of large number of particles occupying fixed positions with respect to each other.

• All particles in a rigid body remain at a fixed distance from one another even after applying forces. Hence there is no change in either shape or dimensions of the body.

• In mechanics, change in either shape or dimensions is not studied. Hence all objects are treated to be perfectly rigid.

• Rigid bodies can have translational motion (rectilinear or curvilinear), rotational motion or a combination of translational and rotational motion. Rigid body can be treated as a particle if it has only translational motion.

• Resultant force acting on any object causes translational motion whereas rotational motion is caused by the net moment of force. Hence rigid bodies can be treated as particles for finding only resultant force. In this case, the dimensions of the body are not required. The dimensions are required to find the moment of force.

• It should be noted that when rigid body is treated as a particle, its mass is supposed to be concentrated at its centre of mass. Newton's laws of motion are applicable to the centre of mass.

Continuum :

• Bodies are assumed to have continuous distribution of matter even though they are made up of particles like atoms and molecules.

• The effects of force on these particles are not studied in mechanics. Instead, the effects on the body treated as a continuum are studied which simplifies the problem.

Point force :

• In reality, when force is applied on any object by another, there is finite non-zero area of contact between the two objects.

• If the area of contact between the two objects is small and can be neglected, the force can be considered as a point force. Such a force is then considered to act only at one point on the object.