15.5: Summary

Conceptual Physics · LibreTexts

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    From LibreTexts, under not declared, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Notation

    \(\propto\) \(\_\_\_\_\) is proportional to

    \(\sim\) \(\_\_\_\_\) on the order of, is on the order of

    Summary

    Nature behaves differently on large and small scales. Galileo showed that this results fundamentally from the way area and volume scale. Area scales as the second power of length, \(A \propto L^2\), while volume scales as length to the third power, \(V \propto L^3\).

    An order of magnitude estimate is one in which we do not attempt or expect an exact answer. The main reason why the uninitiated have trouble with order-of-magnitude estimates is that the human brain does not intuitively make accurate estimates of area and volume. Estimates of area and volume should be approached by first estimating linear dimensions, which one's brain has a feel for.

    15.5: Summary is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.