John Denker suggested saying "cycles per second" rather than "per second" if frequency is what we are talking about. I would presume we would also say "radians per second" rather than "per second" if angular frequency is what we are talking about.
I whole-heartedly agree with this. We should explicitly say what we mean. But this creates the usual problem with dimensionless units... when students are making sure "the units come right" the units in fact won't "come out right" because there is nothing to cancel the dimensionless unit that we explicitly wrote into the paperwork. Students have difficulty dealing with this, and I typically don't have a good solution other than telling them just to learn to live with it.
If we're going to explicitly put dimensionless units into our work (which I indeed prefer), then how do we get students to realize they can take them back out at the appropriate time.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu