Are laws of physics (mechanics) symmetric under uniform rotation?

I'm just starting to learn about symmetry. I understand that physical laws are symmetric under translation and consequently (is it not a consequence?) under uniform velocity in a straight line.

I see that the laws are symmetric under rotation. but are the laws also symmetric under uniform rotation about a fixed axis? You surely can tell if your lab is under a constant rotation about an axis, can't you?

More physically, a frame that rotates uniformly at angular velocity $\omega$ with respect to an inertial one sees a radial force $F=mr\omega^2$ on any body with mass $m$ and distance $r$ to the rotation center. Another inertial force appears: the Coriolis force. They're both present in the rotating frame even when there are no forces appearing in the inertial ones. Thus, the laws of physics are not invariant under the transformations we're considering.