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Why f^2=1/t^2 is because the periods is squared

Hi joeotilio25, to explain why $f^2 = \dfrac{1}{T^2}$, first you need to notice that $f = \dfrac{1}{T}$. Period and frequency are reciprocals of each other, which you can also tell by their units. The units of frequency are "Hz", but "Hz" means "cycles / second". The word cycles is not really a unit, so Hz is essentially "1 / seconds", which is the reciprocal of period which has units of seconds. So, since $f = \dfrac{1}{T}$, when you square both sides you get $f^2 = \dfrac{1}{T^2}$. Squaring both sides was useful for substituting into the centripetal acceleration formula, as shown in the video.

All the best,
Mr. Dychko

Where did revolutions go? I get the answer as 0.39 m-rev/s2.

Hi bbailey1956, that's a good question about where the "revolutions" unit goes. It turns out that "revolutions" is not actually a unit. The wikipedia article on the topic calls "revolutions" a semantic annotation (see https://en.wikipedia.org/wiki/Revolutions_per_minute), which is a fancy way of saying "a word that gives meaning to something else being measured". A good way to look at it is that revolutions are not measured, but rather, the time of a revolution is measured. Only things that are measured (or measurable) get units. The length of a revolution is measurable, and so is the time, but not the revolution itself. To call a revolution a unit would be like measuring the width of a piece of paper and calling "paper" a unit. "Paper" is just a word telling you what was measured.

I can totally see the confusion here, since it's just a habit on this topic of "rpm" to include "rev" among the units in a calculation, even though it is in fact not a unit.

@bbailey1956, I almost forgot to comment on your final answer. I've checked the work, and the answer appears correct, and I can't think of where the mistake would be in your work to have an answer different by a factor of ten, so you'll just have to inspect your work carefully.

All the best,
Mr. Dychko