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‫However, that's not all, because you also need to know how to compute products of inertia, and these

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‫are the formulas for the products of inertia.

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‫And you can see that this equals this.

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‫This equals this and this equals this.

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‫If you compute products of inertia using these formulas, then you will see that this statement holds

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‫true.

7
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‫And so essentially, you could do the same thing with D.M. Let's, for example, take this one so D.M.

8
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‫could be written the density.

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‫That depends on X, Y and Z times.

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‫DEEVEE And you can also see it from the units because the density is kg per cubic meters.

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‫Right.

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‫And then the volume, it's cubic meters.

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‫So if you multiply the density times the volume, then in terms of units it would be kg per meter.

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‫Cute times meter cubed.

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‫This comes from here.

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‫This comes from here.

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‫And you can see that the cube meters will cancel out and you will only be left with a kg and KG is the

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‫unit for D.M. So this statement here perfectly makes sense.

19
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‫But you can also write it out like this role that depends on X, Y and Z, or as a function of X, Y

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‫and Z times.

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‫And instead of Dve, I can write it down like this, the X, D, Y and Z.

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‫And therefore this formula will become like this.

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‫You will have a triple integral X times Z times the density that depends on X, Y and Z.

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‫So in each location, the density of the object could be different.

25
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‫And then times the X, the Y in D.C. and if you have studied calculus, then you know how to compute

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‫triple integrals.

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‫Of course, nowadays you also have a lot of software, a lot of computer programs that do it for you

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‫very quickly.

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‫But still, it's good to know fundamental formulas behind it.

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‫And now if your object is mass symmetric like this one, and in fact it should be mass symmetric about

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‫all axis and about the Y axis and about the X axis, because you can also rotate this tube like this

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‫and like this, not only like this.

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‫So if this object is mass symmetric about all of its axis, then the products of inertia will become

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‫zeros.

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‫So if you go through this process here, then you will see that it will become zero and that would apply

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‫for this and for this.