Dear Herb + others:
Reading this heated discussion I understand why students get confused!
The cure? Stick to basics!
There are two surfaces in contact (say, "object" and "support"),
and the force transmitted has the N=normal and T=tangential components
(each of these appear in opposite pairs, according to action-reacton).
If there is no sliding the friction force T=<mu0 N, whatever is needed
to prevent sliding (otherwise what would be the friction force on an
object sitting quietly on a horizontal table?). If there IS sliding,
the friction force T=mu N, in a direction opposed to the relative
motion. And That's all, folks!
I like to add something about "rolling friction", as for example
when you roll a wheel (without the car, just the wheel with tire).
You may draw an exaggerated picture of an underinflated tire making
contact with the floor over a significant extent of its outside.
The picture might suggest that in order to start the rolling motion,
you must push the wheel so that the sum of push + weight falls
outside the surface of support (= contact tire/floor). THIS IS WRONG.
On this surface of contact, the tire is flat and just transmits the
internal air pressure, which is NORMAL to the floor and cannot
generate any friction force! This is the reason why an underinflated
baloon will roll down an inclined plane even for a slight angle.
Regards Emilio