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

C4.1 Centre of Mass

We’ve been looking at weights as point loads. But mass/objects in reality occupy a volume, and therefore the weight is acting in a distributive manner rather than as a point load.

However we can still treat it as a point load if we find a point in the mass which represents the effective single point where the total weight is acting on. This is called the centre of mass (CoM).

It is useful to find the CoM as it helps us to simplify our statics calculations:


Using centre of mass to represent distributed load to simplify static analysis

C4.1 Centre of Mass

We’ve been looking at weights as point loads. But mass/objects in reality occupy a volume, and therefore the weight is acting in a distributive manner rather than as a point load.

However we can still treat it as a point load if we find a point in the mass which represents the effective single point where the total weight is acting on. This is called the centre of mass (CoM).

It is useful to find the CoM as it helps us to simplify our statics calculations:


Using centre of mass to represent distributed load to simplify static analysis

The next question is, how do we calculate the CoM? Thanks to Isaac Newton, we can use integration to evaluate our CoM:

Formula to calculate centre of mass in x and y directions

There will be no examples for this section, as CoM is of more interest in Dynamics. In Statics, we’re more interested in centroids.

The next question is, how do we calculate the CoM? Thanks to Isaac Newton, we can use integration to evaluate our CoM:

Formula to calculate centre of mass in x and y directions

There will be no examples for this section, as CoM is of more interest in Dynamics. In Statics, we’re more interested in centroids.

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