Mechanics- Polar Co-ordinates

Question

Recently we were taught about uniform circular motion and polar co-ordinates.

For our homework we got an assignment with the position vector of an ellipse, expressed with $t$ as time. e.g. $4 \cos(2t) \hat{i} + 3 \sin(2t) \hat{j}$

We haven't really covered ellipses before and have just started this mechanics module. We are supposed to find the magnitude of the radial and transversal components of the velocity in polar co-ordinates, when $t$ is equal to a specific number.

I have no idea how to derive an equation for $r$ and $\theta$ for an ellipse and thus derive the velocity expressed by radial and transversal components. I am just curious as to how one would find the $r$ and $\theta$.

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score 0 · Accepted Answer · answered Oct 18 '21 at 11:10

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$$x = 4cos(2t)$$ $$y = 3sin(2t)$$ Can you find polar coordinates now? $$r^2=x^2+y^2$$ $$tan \theta = y/x$$

answered Oct 18 '21 at 11:10

Tojra

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Thank you! I actually did find this... but for some reason I thought it was wrong, I can't even remember why. Maybe it's because I was working at 11pm ahahaha. – Lars Oct 18 '21 at 15:18

Mechanics- Polar Co-ordinates

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