Just a heads-up, although moment of inertia (MoI) won’t be used much in this Statics course, it is included because it’s part of the Statics course syllabus that is followed by almost all universities across the world.
It’s an abstract concept; suffice to say that there are both mass MoI and area MoI, each briefly described below:
In statics and solid mechanics, the geometrical or area moment of inertia is of more interest. The formula is given as follows:
Just a heads-up, although moment of inertia (MoI) won’t be used much in this Statics course, it is included because it’s part of the Statics course syllabus that is followed by almost all universities across the world.
It’s an abstract concept; suffice to say that there are both mass MoI and area MoI, each briefly described below:
In statics and solid mechanics, the geometrical or area moment of inertia is of more interest. The formula is given as follows:
Note that the units for MoI is m^{4} (y^{2} [m^{2}] × dA [m^{2}] = m^{4}). Sometimes it might be more convenient to express the units as mm^{4}.
When calculating MoI, setting the reference axis correctly is of utmost importance. The reference axis is where you take your y or x variables from (in the I_{x} = ∫y^{2} dA and I_{y} = ∫x^{2} dA formulas).
Calculating your MoI from either the x_{1}-x_{1} or x_{2}-x_{2} references axes will give you different values of MoI. You need to be certain of the reference axis that the question is asking you to calculate your MoI from.
Let’s look at an example now to illustrate this. Again, the examples are designed to show you the derivation of the moment of inertia formula for some of the common shapes. However in practical situations, you can usually referring to the table of moment of inertia formulas instead.
Note that the units for MoI is m^{4} (y^{2} [m^{2}] × dA [m^{2}] = m^{4}). Sometimes it might be more convenient to express the units as mm^{4}.
When calculating MoI, setting the reference axis correctly is of utmost importance. The reference axis is where you take your y or x variables from (in the I_{x} = ∫y^{2} dA and I_{y} = ∫x^{2} dA formulas).
Calculating your MoI from either the x_{1}-x_{1} or x_{2}-x_{2} references axes will give you different values of MoI. You need to be certain of the reference axis that the question is asking you to calculate your MoI from.
Let’s look at an example now to illustrate this. Again, the examples are designed to show you the derivation of the moment of inertia formula for some of the common shapes. However in practical situations, you can usually referring to the table of moment of inertia formulas instead.