And the simple physics thereof:
I can assure you that any roped free climber, regardless of experience or ability, on a serious and committing friction lead has known the fear to which my title refers. This subject comes to mind in the wake of Daniel Duane’s recent brilliant piece in the New York Times  on Alex Honnold’s free solo ascent of Freerider on El Cap. In it are evocations of the primal fear of having to trust the shoes while the hands are essentially useless, and of the fatal urge to lean in toward the false comfort of the cliff face.
A climber can easily sense any small increase in steepness which might lead to a slide:
“It still felt really insecure and I still always felt like the feet might slip,” [Honnold] said …
According to the Web the coefficient of friction of a climbing shoe sole in contact with various rock surfaces varies from 0.9 to 1.1 and is often higher if the surface is particularly rough. For my purpose here I will use a coefficient value of one.
This means, for example, that a shoe vertically loaded on a featureless forty-five degree slope has a friction resistance just balancing its tendency to slide. In this case there is no margin for error and to lean in from the vertical, however little, without foot slippage is virtually impossible. Slopes steeper than this are theoretically unclimbable by stepping-up alone, although there are steeper ones (on the Big Stone and elsewhere) with unusual roughness, or that yield to dynamic techniques, or to raw courage.
Desperate dynamic moments entail stepping up faster than the feet slide down, but have no place in controlled free soloing. Nor are we considering slopes with tiny ledges, or scoops, or places where the hands can do anything other than lightly kiss or even leave the face. Even roped, the friction leader has scant opportunity to set protection owing to a general featurelessness of slabs.
More commonly one is on a lesser slope, say of thirty degrees, as is typical of our own White Horse Ledge in New Hampshire. Here the geometry is more forgiving although it takes real conviction to be convinced of it. In this case one need lean in from the vertical only fifteen degrees for the feet to give way.
Amazingly Alex learned to control the fierce reluctance to stand free, in effect, putting his hands in his pockets and tip-toeing to the next haven a dozen steps above.
Two-thousand feet above the Yosemite Valley floor!
Without a rope!
New York Times, Daniel Duane: “El Capitan, My El Capitan”