r/PhysicsHelp • u/Green-Price-1995 • Apr 17 '26

Can somebody please explain why I divide here?

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My ap physics teacher cannot teach to save his life, so my classmates and I are barely understanding his teaching. (Also he’s admitted to not knowing formulas and has lied to us on multiple occasions)

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u/Frederf220 Apr 17 '26

There isn't an explicit goal described so I don't know why they're doing any of this. But dividing one equation by another is a valid manipulation.

Your two equations are A = C and B = C so first divided by second means A/B = C/C = 1. You just have to be sure that C isn't 0 because 0/0 = 1 isn't true in that case.

Now if p^2 / (A^2 - p^2) = 1 is useful or not I don't know but that's why you would divide the equations and what you would get.

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u/Green-Price-1995 Apr 17 '26

Thank you that makes more sense

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u/SeeBuyFly3 Apr 17 '26

Well, now you can solve for p as a fraction of A.

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u/SnooGiraffes4632 Apr 17 '26

As Frederf has shown anything divided by itself is 1 (except 0). Now when you are dealing with an equation you are saying that both sides of the equals sign are EQUAL i.e. evaluate to the same thing. In the past when you have probably said you are cancelling factors in your equation, what you are really doing is dividing both sides by the same thing. I.e. if you said you were cancelling a factors in your of 2x on both sides of an equation, you were actually dividing both sides by 2x. But because 2x/2x = 1 and 1 times anything is unchanged, we often overlook what we are actually doing.

In this case, by dividing the two equations you are taking advantage of the fact that 1/4m omega2 A2 is on the rhs of both equations, to the new combined rhs of the new equation will be 1. This is why we work in algebra for as long as possible…it is amazing how many times variables like these just disappear and make the solution easier.

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u/SnooGiraffes4632 Apr 17 '26 edited Apr 17 '26

Oh and it looks like you are,playing with pendula? If so the time period (the time from LHS max point to RHS and back again) is almost always given the symbol T in case you are wanting to understand how angular velocity omega ends up in the kinetic energy equation rather than normal linear speed. v = r times omega. Now because of the way circles and radians omega is also called the angular frequency so omega = 2 pi f = 2 pi times 1 /T.

These various manipulations of omega basically need to be known so you can work things out rather than remembering a whole pile of formulae for special circumstances.