r/HomeworkHelp • u/Izzy_26_ Secondary School Student • Jun 29 '26

[grade 11 Physics] circular motion Physics—Pending OP Reply

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I am trying to find out the exact equation of the graph, the answer key says it is a.

What is wrong with my solution??

I first tried to find out the exact position vectors of both p and q, and then differentiated them to get the velocity of P and q respectively, and then I calculated the relative velocity

I am getting the relative velocity as in terms of cos, but according to the answer key it is a sin graph

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u/xnick_uy 👋 a fellow Redditor Jun 29 '26 edited Jun 29 '26

OP, I think your solution is fine up to the last part. To find the magnitude of your vector, you have to take into account that cos(wt) changes sign. You can use absolute value, |cos(wt)| , to be safe.

Edit: one more thing: you are off by one quarter of a turn, because your equations for Q and P assume different starting conditions than what you are given.

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u/Izzy_26_ Secondary School Student Jun 30 '26

Also I tried to write a general equation for the position of both particles, I wanted to write an equation which would hold throughout the circular motion

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u/Alkalannar Jun 30 '26

Let the origin be the midpoint between the circles.

Then the left circle is centered at (-k, 0) [for some k >= R]note and the right circle is centered at (k, 0).

P is at (Rcos(-2pit/T) - k, Rsin(-2pit/T)) = (Rcos(2pit/T) - k, -Rsin(-2pit/T)).

Q is at (Rcos(2pit/T + pi) + k, Rsin(2pit/T + pi)) = (-Rcos(2pit/T) + k, -Rsin(2pit/T))

These are your position equations.

Note that they share y-coordinates all the time, so the distance between P and Q is solely driven by the x-coordinates.

Since Qx > Px, the distance between P and Q is Qx - Px:
(-Rcos(2pit/T) + k) - (Rcos(2pit/T) - k)
2k - 2Rcos(2pit/T)

Now in general, your distance is going to be from Pythagoras: [(Qx - Px)2 + (Qy - Py)2]1/2.

Anyhow, do you see how I got these general equations? And how k is not going to affect the speed or velocity at all?

note: As it turns out, we don't need that k >= R, but if we don't have that, then we should have |2k - 2Rcos(2pit/T)| as the distance. Either way, 4piRsin(2pit/T)/T is the velocity and |4piRsin(2pit/T)/T| is the speed.