The moment of inertia of a rectangular section 3 cm wide and 4 cm deep about X-X axis passing through center is ____

Concept:

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 2^nd moment of area or 2^nd 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: