Significance of the angle theta at r=0 point

[C. Lee]

Hello,

I was working on a classical mechanics problem, and I suddenly came up with this question:

Let's think about a point in a 2-D plane. This point is represented by (r, θ), where r is the distance between the origin and the point and θ is the angle measured from the x-axis.

Now, what is the significance of the angle θ if r=0?

Personally, I do not think θ has any significance because θ do not affect any property of the point since it is located exactly at the origin. To me, it makes no sense at all to specify a point at the origin with an angle.

Is there any case where θ has any physical(or mathematical) significance although r=0?

 

[pbuk]

Is there any case where θ has any physical(or mathematical) significance although r=0?

No. We usually define the origin as the point (0, 0) and leave the points (0, θ) where θ ≠ 0 undefined.