Center of gravity

Center of gravity
Figure 1.1 Centre of gravity

You must have seen a circus artist doing a tight rope walk. Ever wondered how he manages to walk on a rope without falling down and why he stretches his hands or holds a long bamboo pole while doing so? You must also have seen a rolly-polly doll which always stands erect even if it is tilted to a side and left. These effects can be understood by the study of the concept of centre of gravity and equilibrium of bodies.

An extended body is made up of a large number of particles. In the case of rigid bodies the relative position of these particles does not change. Each of these particles is attracted by a force towards the centre of the Earth called weight of the particle.

The weight of each particle of the body acts downwards . If W1, W2, W3,…… are weights acting on particles P1, P2, P3, ……. of the body, respectively, the resultant weight of the body is given by the sum of individual weights, W = w1 + w2 + w3 + …..

The resultant weight (W) appears to act through a fixed point irrespective of the position or the orientation of the body. This fixed point is called centre of gravity and is denoted as G. The centre of gravity of a body is defined as the point through which the weight of the body acts.

Activity

Center of gravity - Metre scale
FIGURE 1.2 Center of gravity – Metre scale
  1. Suspend a metre scale at one end by means of a string. The scale does not remain horizontal.
  2. The scale remains horizontal and stable when it is suspended at the centre .

This point on the scale is the centre of gravity of the scale. The centre of gravity may lie within the body or outside it. If a body is suspended at its centre of gravity, it remains in a balanced state. This fact can be used to rest if a given point in a body is its centre of gravity or not.

Centre of Gravity of Regular Bodies

The centre of gravity of a body depends on the shape and size of the body.

1. The centre of gravity of a square lamina or a rectangular lamina is at the point of intersection of its diagonals.

Center-of-gravity-Rectangular-lamina
FIGURE 1.3 Center-of-gravity-Rectangular-lamina

2. The centre of gravity of a circular plate lies at its centre.

Centre of gravity - Circular plate
FIGURE 1.4 Centre of gravity – Circular plate 

3. The centre of gravity of a triangular lamina is at the point of intersection of its medians (centroid).

FIGURE 1.5 Centre of gravity - Triangular lamina
FIGURE 1.5 Center of gravity – Triangular lamina

4. The centre of gravity of sphere is at the geometric centre of the sphere.

centre of gravity - Sphere
FIGURE 1.6 Center of gravity – Sphere

5. The Centre of gravity of a solid right circular cone of height ‘h’ lies on its axis at a distance (h/4) from its base.

Center of gravity - Right circular cone
FIGURE 1.7 Center of gravity – Right circular cone

6. The center of gravity of a cylinder is at the midpoint of its axis.

Center of gravity - Cylinder
FIGURE 1.8 Center of gravity – Cylinder

7. The centre of gravity of two right circular cones of equal height and jointed at the base is at the centre of base of either cone.

Center of gravity - Right circular cone
FIGURE 1.9 Center of gravity – Right circular cone

8. The center of gravity of an annular ring is at its geometric centre. 

Center of gravity - Annular ring
FIGURE 1.10 Center of gravity – Annular ring

Centre of gravity of an Irregular Lamina

Centre of gravity - Irregular shaped lamina
FIGURE 1.11 Center of gravity – Irregular shaped lamina

The centre of gravity of an irregular lamina is determined by suspending it at any three different points near its edge and drawing lines from the point of suspension along the plumb line. The point of intersection of the three lines gives the position of the centre of gravity, as shown in the Fig 1.11.