How do you know a force if a force is radially symmetric?

[Elvis 123456789]

If a force only depends on a radial distance "r" and it only has a radial component in the "e_r" then is it radially symmetric? This pertains to some homework problem I have, but part of the problem is that I'm not exactly sure what is meant by "radially symmetric". I assume its asking if the force is the same at any point on a circle of radius "r". If the force only depends on "r" and its only in the radial direction then it would be radially symmetric, correct?

 

[Simon Bridge]

If a force only depends on a radial distance "r" and it only has a radial component in the "e_r" then is it radially symmetric?

Yes.

This pertains to some homework problem I have, but part of the problem is that I'm not exactly sure what is meant by "radially symmetric". I assume its asking if the force is the same at any point on a circle of radius "r". If the force only depends on "r" and its only in the radial direction then it would be radially symmetric, correct?

It is radially symmetric if the field maps onto itself under rotations. It is likely, if this is the first you've heard the term, that the specific symmetry being considered is that rotating the coordinate axes makes no difference to the expression for force.
This is also called "rotationally symmetric".

Note:
1. the B field about a wire carrying a current is radially symmetric - even though it does not point in the radial direction.
2. there are different amounts of radial symmetry