Using polar coordinates in 1-dimensional problems

[kent davidge]

If I have a physical problem, say, a particle which is constrained to move in the $y$ direction, which means that its $x$ coordinate remains fixed, does it make sense to write $y$ in terms of polar coordinates? That is, $y = r \sin\theta$. Since now I have two parameters $r,\theta$ varying, so this has only made solving the problem harder than it must be, right?

 

[Nugatory]

so this has only made solving the problem harder than it must be, right?

Yes.

 

[anorlunda]

We choose coordinate systems to be convenient. Some choices can be very inconvenient.

 

[Orodruin]

If I have a physical problem, say, a particle which is constrained to move in the $y$ direction, which means that its $x$ coordinate remains fixed, does it make sense to write $y$ in terms of polar coordinates? That is, $y = r \sin\theta$. Since now I have two parameters $r,\theta$ varying, so this has only made solving the problem harder than it must be, right?

If you do this, only one of your polar coordinates will be a free parameter as the other will be fixed. For example, consider the line $x = 1$. On this line, $r^2 = 1 + y^2$ which means that, if you fix $\theta$, then $r^2(1-\sin^2\theta) = 1$ and so $r = 1/\cos\theta$. The relation between $y$ and $\theta$ is therefore $y = \tan\theta$, which is just a (non-linear) change of parametrisation of your line.