Centre of Gravity and Moment of Inertia:

This unit shall help you in understanding the concepts of centre of gravity of wires, thin uniform plates of several shapes with or without openings and simple solids such like cone, sphere and cylinders. The concept of centroid of plane areas is same to the centre of gravity of thin uniform plates of same shape like the plane areas. Moment of Inertia of plane areas around any given axes is mathematically referred to as second-moment of areas. The knowledge of the moment of inertia of plane areas is useful in the analysis of bending stresses of beams under flexure. The moment of inertia of discs, rods or spheres are useful in studying the problems in dynamics of rigid-bodies.

Objectives

After learning this unit, you must be able to determine

• location of centre of gravity of uniform-wires of several shapes,
• location of centre of gravity of masses of plates of several shapes with or without openings,
• the volume plus surface areas of sevearl simple solids and their location of centre of gravity using two theorems given by Pappus & Guldinus, respectively, and
• Moment of inertia of numerous areas about the given axes.