Today I was reading a book for high school physics and in that book it was written that the center of mass of an object can be real or virtual i.e. it may or may not have mass at that point, however, I am unable to understand that how could COM be virtual? Do we assume it such so that it is easier to solve problems? Any help or insight will be appreciated!
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5$\begingroup$ The COM of a horseshoe would be non material. $\endgroup$– Adrian HowardCommented Aug 26, 2021 at 4:55
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3$\begingroup$ Or a doughnut (i.e. the center is in the hole) $\endgroup$– JosephDoggieCommented Aug 26, 2021 at 16:16
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5$\begingroup$ This is not, in my opinion, a common or particularly useful term. What book is this? $\endgroup$– trentCommented Aug 26, 2021 at 18:20
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3$\begingroup$ I agree with trentcl. Since the centre of mass is a single point, it has zero volume, so it doesn't actually matter whether there is mass there. $\endgroup$– SandejoCommented Aug 26, 2021 at 21:22
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By "virtual" the author means "non-material." The center of mass can be a material point or a non-material point.
For example, the center of mass for a solid sphere is a material point. It is coincident with a material point of the body.
The center of mass for a hollow sphere is a non-material point. It floats in space and is not coincident with a material point of the body.
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9$\begingroup$ A donut also works well to visualize this. $\endgroup$– bluesCommented Aug 26, 2021 at 12:51
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6$\begingroup$ A sphere is hollow: all points equal (not less than or equal) to the radius distance. A ball is the solid shape. $\endgroup$– JDługoszCommented Aug 26, 2021 at 15:00
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11$\begingroup$ @JDługosz erm, maybe in some other world language, but I think you'd have trouble convincing an English native speaker of the validity of your claim "a sphere is hollow, a ball is solid".. Evan's use of "hollow sphere" and "solid sphere" is a correct distinction $\endgroup$ Commented Aug 26, 2021 at 16:08
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4$\begingroup$ @CaiusJard In mathematics, "ball" for the solid object and "sphere" for the hollow object is the standard terminology. Outside of mathematics (even in physics), "sphere" is usually used for both. $\endgroup$ Commented Aug 26, 2021 at 17:00
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2$\begingroup$ It is vastly safer to refer to "hollow sphere" or "surface of a ball", to disambiguate from "solid ball", in mathematical practice, in my experience. Sure, sometimes context makes it clear, but there's no completely universal time-invariant convention. $\endgroup$ Commented Aug 26, 2021 at 18:10