Basics of Kinetics of Rigid Bodies:

Certain geometrical properties associating to the mass of the body are referred to repeatedly in this study. Thus, we shall study these properties in detail before proceeding for further development.

The prerequisite for this study is the concept of a rigid body, kinematics of a particle and kinetics of a rigid body. We know from the principle of the motion of the mass centre that the relation among R (the resultant force) and the linear acceleration of the mass centre is expressed by

                                                     R = ma = (W/g) a.

Any resultant couple ∑ M G causes an angular acceleration α and from the kinematics study, we get the relation between a and α. Further we shall show that

                                                         ∑ M _G = I _G α

where,

I _G = mass moment of inertia of the body.

The possible effects of the resultant force and couple system on a rigid body at rest may be reviewed as below. If the resultant is a single force that passes out through the mass centre, we know that a motion of translation occurs. A force system whose resultant is a couple shall cause the body to have the motion of rotation about its centroidal axis; and, when the resultant is both a force and a couple the plane motion consists of both, a linear motion of the mass centre and an angular acceleration. The angular acceleration is a property of the body and is independent of the actual axis of rotation.

Objectives

After studying this unit, you should be able to :

• Compute mass moment of inertia for various bodies,
• understand motion of rotation of a rigid body about a fixed axis, and
• Solve problems regarding plane motion of several rigid bodies involving rod, sphere, disc, pulley etc.