change center of rotation

How does one specify the center about which an object can be rotated?

I have obtained several objects as the result of separating what used to be a single
object into its constituent parts, and now I want to rotate one of those
parts (one of the new objects I obtained by way of the separation process).

My problem is that the center for rotation of the part is extremely inconvienient…
how can I change the center of rotation to make it reasonable (like the
barycenter of the vertices, for example), or, even better, how can I specify it
to be an arbitrary point?

Thanks

dpaddy

1- is the menu bottom header

2 - right beside it you can choose between center of individual objects
or center of the whole group

Saluations

YES!!!

I place the 3D cursor at the desired center of rotation,
and then I specify the 3D cursor within the drop down menu
which is activated by clicking on the leftmost of the two
icons you indicated.

Thanks!

Another tip is that if you CTRL-CLICK when you reposition the 3D cursor, it will snap to the grid.