TABLE OF CONTENTS The centroid of an area is situated at its geometrical centre. In each of the following figures G represents the centroid, and if each area was suspended from this point it would balance.
The centre of gravity of a body is the point at which all the mass of the body may be assumed to be concentrated and is the point through which the force of gravity is considered to act vertically downwards, with a force equal to the weight of the body. It is also the point about which the body would balance.
The centre of gravity of a homogeneous body is at its geometrical centre. Thus the centre of gravity of a homogeneous rectangular block is half-way along its length, half-way across its breadth and at half its depth.
Let us now consider the effect on the centre of gravity of a body when the distribution of mass within the body is changed.
Consider a rectangular plank of homogeneous wood. Its centre of gravity will be at its geometrical center: i.e., half-way along its length, half-way across its breadth, and at half depth. Let the mass of the plank be W kg and let it be supported by means of a wedge placed under the centre of gravity as shown in Figure 2.2. The plank will balance.
Now let a short length of the plank, of mass w kg, be cut from one end such that...
