- Centre of Mass & Centre of Gravity
Consider a uniform rod of length L. When the rod is placed horizontally, each particle of the rod is pulled by the gravitional force of the earth. The sum of all three forces will be equal to the total weight of the rod.
Consider two systems: One is the rod AB of weight W and other is a concentrated weight W, at a distance 1/3 L from point A.
These two systems are equivalent as far as the net gravitational pull is concerned, but the moment of the gravitational forces of the two systems about point A is different.
- Second Moments and the product of area of a plane
The second moments of the area A about the x and y axes denoted as Ixx and Iyy , respectively are defined as:
Note that,
(1) The first moment of area can be positive or negative, whereas the second moment of area is positive only.
(2) The element of area that are farthest from the axis contribute most to the second moment of area.
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