Physics - Polar Coordinates: Describe the locus of points

[bobraymund]

Hi,

So, I was doing my physics summer work and had no idea what the following question was talking about:

Homework Statement

For the following polar coordinate points:

(4, 0) (4, 60) (4, 90) (4, 135) (4, 180) (4, 270)

Describe the locus of points for which

a) r = 4
b) r = a

An image, for reference, can be seen http://img43.imageshack.us/img43/6422/0815002025.jpg .

The Attempt at a Solution

I was thinking that the answer would be merely saying something like (4, 0) (4, 60) (4, 90) (4, 135) (4, 180) (4, 270), because those are all the points at r = 4. But I have no idea. :(

Thanks for the help!

 

[rl.bhat]

The locus of the points is a circle with center (0, 0) and radius 4.

 

[bobraymund]

Ah, thanks! that makes sense!

So, then this one here: http://img413.imageshack.us/img413/6007/0815002113.jpg

Would that be a line with like slope ?

Edit: the second question states: describe the locus of points for which theta = 60 and theta = theta1 (where theta1 is a fixed angle)

 

[rl.bhat]

Yes. It is a straight line.

 

[rwisz]

Hi there,

Don't worry, polar coordinates can be a bit confusing at first. To answer your question, the locus of points for which r = 4 is a circle with radius 4 centered at the origin (0,0). This is because in polar coordinates, r represents the distance from the origin to a point, and when r is constant, it creates a circle. So, in this case, the points (4, 0), (4, 60), (4, 90), (4, 135), (4, 180), and (4, 270) all lie on a circle with radius 4 centered at the origin.

For the second part, where r = a, the locus of points would be a circle with radius a centered at the origin. This is because a is a variable, so the circle could have any radius depending on the value of a. Again, the points (4, 0), (4, 60), (4, 90), (4, 135), (4, 180), and (4, 270) would all lie on this circle, but it could have a different radius than the one in the first part.

I hope that helps clarify things for you. Keep up the good work with your summer physics work!