What is the origin of the term "moments" in the study of random variables?

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I understand what the moments are, I just want to know who picked the term "moment" and why? How is the word "moment" related to different but related ways to describe the shape of a random variable?

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I don't think you'll find anything much better than this: Earliest Known Uses of Some of the Words of Mathematics says

Moment was taken into Statistics from Mechanics by Karl Pearson when he treated the frequency-curve (or observation curve) as the sheet enclosed by the curve and the horizontal axis. See his "Asymmetrical Frequency Curves," Nature October 26th 1893: "Now the centre of gravity of the observation curve is found at once, also its area and its first four moments by easy calculation." (OED2).