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I am a bit confused about how to determine which strips to consider when calculating the $\text{COM}$ of certain objects.

For example, when we calculate the $\text{COM}$ of a semi circle solid of radius $R$, we usually orientate it about the $x$ axis with the $\text{COM}$ on the $x$ axis.

Strips are then chosen to go vertically down the semi circle. Why? Why don't we choose it going horizontally for example?

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    $\begingroup$ The short answer is you can chose whatever strips you desire as long as you can take the integrals. At the end of the day you are taking a multiple integral. Perhaps, symmetries in the problem, make the calculations easier in some cases than the others. $\endgroup$
    – Ali
    Commented Mar 15, 2017 at 18:18
  • $\begingroup$ @Ali why does taking them vertically make the integral easier? $\endgroup$
    – PhysicsMathsLove
    Commented Mar 15, 2017 at 18:36
  • $\begingroup$ It doesn't make it easier for a circle really (since it's the same either way). The difference will have to do with how things work out in terms of using x values or y values. $\endgroup$
    – JMac
    Commented Mar 15, 2017 at 19:22

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Well, as Ali said in the comment, there really isn't a general preference in choosing "stripes". We usually chose which equation is easier to integrate. For example an object like in the figure below might be represented by an equation like $y = 4-x^2$. Graph of $y = 4-x^2And choosing to use vertical stripes and integrating y with x is going to be easier than using horizontal stripes. As in the case of a uniform circular disc, both choices are equally straightforward. Maybe the reason vertical stripes were used is because we usually integrate y over x.

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