Question
Download Solution PDFThe moment of inertia of a rectangular section 3 cm wide and 4 cm deep about X-X axis passing through center is ____
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Area Moment of Inertia:
- It is a geometrical property of an area which reflects how its points are distributed with regards to an arbitrary axis.
- It is also known as 2nd moment of area or 2nd Moment of Inertia.
- Its SI unit is ‘m4’
- Mathematically, it is represented as
\({I_x} = \int\!\!\!\int {y^2}\;dxdy\;\;and\;\;\;{I_y} = \int\!\!\!\int {x^2}dxdy\)
Calculation:
Given:
width(b) = 3 cm, height(h)= 4 cm
For the rectangular section, the Moment of Inertia is given by
\({I_{xx}} = \frac{{b{h^3}}}{{12}} = \frac{{3 \times {4^3}}}{{12}} = 16\;c{m^4}\)
Mass Moment of Inertia:
It is a measure of the resistance of a body to angular acceleration about a given axis that is equal to the sum of the products of each element of mass in the body and the square of the element’s distance from the axis.
It’s SI unit is kg-m2
Mathematically, \(I = \mathop \sum \limits_{i = 1}^n {m_i}r_i^2\)
MOI of Some Standard Shapes:
Type of Shape |
Moment of Inertia |
Rectangle |
\({I_{xx}} = \frac{{b{h^3}}}{{12}},\;\;{I_{yy}} = \frac{{h{b^3}}}{{12}}\) |
Triangle |
\({I_{C.G}} = \frac{{b{h^3}}}{{36}}\;,\;{I_{base}} = \frac{{b{h^3}}}{{12}}\) |
Circle |
\({I_{xx}} = {I_{yy}} = \frac{\pi }{{64}}{d^4}\) |
Semicircle |
\({I_{xc}} = 0.393{r^4}\;,\;\;\;{I_{yc}} = 0.11{r^4}\) |
Last updated on Jun 7, 2025
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