Consider a thin lamina of area A and its differential area dA is shown in Fig. 7.1
Suppose dA is at a distance of x from y-axis and y distance from x-axis
Its distance from point O is r
For calculating are a moment of Inertia about x-axis for dA is given by,
dIx = y2dA
Total moment of inertia can be given by,
Ix = x = 2 dA
Similarly, for y-axis, total moment of inertia is given by,
Iy = y = 2 dA
For z-axis,
Moment of inertia can be written as-
dIz = r2dA
Total moment of inertia can be given by,
Iz = z = 2 dA
Thus, we get
Ix = 2 dA
Iy = 2 dA
Iz = 2 dA
= 2 + y2) dA
= 2dA + 2 dA
= Ix + Iy
This can also be written as
i.e.,
Iz = Ix + Iy
Note:
S.I. unit of area moment of inertia is L4
Where,
L = Length (m) = m4
Links of Previous Main Topic:-
- Introduction to statics
- Introduction to vector algebra
- Two dimensional force systems
- Introduction concept of equilibrium of rigid body
- Friction introduction
- Introduction about distributed forces
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