Centre of Gravity

Centre of Gravity

From the molecular theory of matter, all matters are made up of small or tiny particles which are equal in mass m. each of these particles are pulled towards the earth with force or weight mg. therefore the earth pull on all matters is the sum of the earth pull on individual particles. The resultant of these forces is the resultant earth pull on a body.

Mg= mg + mg+ mg+ mg+……………

Where M = m + m+m+m---------

The sum of mg gives the resultant Mg      See Fig 1

The centre of gravity of a body is the point at which its resultant weight acts.

The centre of gravity of a uniform and symmetrical objects is at the centre of the body

For example,       

1. The centre of gravity of a circular object is at the centre
2. The centre of gravity of a ball or sphere is at the centre
3. The centre of gravity of a meter rule is at 50cm mark
4. The centre of gravity of a rectangle , squre, or parallelogram is at the intersection point of the diagonal

To find the Centre of gravity of irregular objects ,the following methods can be used.

1.  By using plumbline e.g plane sheet of material
2. By using balancing method e,g meter rules

Example

A uniform bar with weight 10N rest on two supports A and B as shown in figure 1 above . Calculate the upward reaction at A and B

SOLUTION

See fig 2

A+B =30+10+5=45

Taking moment about A

B X 7 + 30 X 2= 10 X 3 + 5 X 8

7B +60=30+40

7B=10

B=10/7=1.4N

A + B=45

A=45-10/7= 43.57N

The above solution could be solved by taking moment at B OR any other point.

Also moment of A reaction at point A =0

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