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I'm a little confused by your statement about friction and normal forces.
For no slipping, we have static friction, which is not proportional to
normal force anyway. Did you intend that the maximum static friction is
not proportional to the normal force?
Nothing wrong. See:>general have the condition that the friction is directly proportional
and references therein. It comes about because you simultaneously
have to consider forces and torques, because linear acceleration =
radius * angular acceleration for no slipping. Thus we do *not* in
to normal force and other "common" rules about friction.
This particular example is a favorite counter-example of mine to the
question: Is friction always opposite to the direction of an applied
force (in the absence of horizontal forces other than friction and
the applied force)?
This problem is also a wonderful case study in the careful
distinction between pseudowork and real work. See Chabay & Sherwood's
If a constant force is applied tangentially to a rolling cylinder in the
direction in which the cylinder is rolling by means of a horizontally
unrolling line wrapped round the cylinder,
won't that line move twice as fast as a line which applies a force of
of the same magnitude in the same direction (say by a wire halter and axle)
at the height of the center of the cylinder?
If the distance of application is doubled in unit time for unit force
that indicates more power?....