engineering core courses

Statics
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Statics
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C4: Centre of Mass, Centroids, Moment of Inertia
4.1 Centre of Mass
- Theory
4.2 Centroids
- Theory - Example - Question 1 - Question 2 - Question 3 - List of centroids for common shapes
4.3 Centroid of Composite Bodies
- Theory - Example - Question 1 - Question 2 - Question 3
4.4 Moment of Inertia
- Theory - Example - Question 1 - Question 2 - List of moment of inertia for common shapes
4.5 Parallel-Axis Theorem
- Theory - Example - Question 1 - Question 2

C4.4 Moment of Inertia

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:

  • Mass moment of inertia – quantity that resists the angular acceleration of a body when torque is applied. From another viewpoint, it also means it is able to store more rotational energy with a larger mass MoI. This quantity is usually used more in Dynamics.
  • Area moment of inertia – also known as the 2nd moment of area, this quantity governs the stress along a cross-section when subjected to bending and torsion. This will be covered more in Solid Mechanics I.

In statics and solid mechanics, the geometrical or area moment of inertia is of more interest. The formula is given as follows:

C4.4 Moment of Inertia

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:

  • Mass moment of inertia – quantity that resists the angular acceleration of a body when torque is applied. From another viewpoint, it also means it is able to store more rotational energy with a larger mass MoI. This quantity is usually used more in Dynamics.
  • Area moment of inertia – also known as the 2nd moment of area, this quantity governs the stress along a cross-section when subjected to bending and torsion. This will be covered more in Solid Mechanics I.

In statics and solid mechanics, the geometrical or area moment of inertia is of more interest. The formula is given as follows:

Moment of inertia formula

Note that the units for MoI is m4 (y2 [m2] × dA [m2] = m4). Sometimes it might be more convenient to express the units as mm4.

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 Ix = ∫y2 dA and Iy = ∫x2 dA formulas).

Reference axis for moment of inertia

Calculating your MoI from either the x1-x1 or x2-x2 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.

Moment of inertia formula

Note that the units for MoI is m4 (y2 [m2] × dA [m2] = m4). Sometimes it might be more convenient to express the units as mm4.

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 Ix = ∫y2 dA and Iy = ∫x2 dA formulas).

Reference axis for moment of inertia

Calculating your MoI from either the x1-x1 or x2-x2 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.

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