What does frictionless pulley really mean?

[andyrk]

When we say "pulley is frictionless", do we mean its groove where the string moves or its axle or both?

 

[mfb]

The axle - but if you can neglect kinetic energy of the wheel, a frictionless groove gives the same result.

 

[andyrk]

The axle - but if you can neglect kinetic energy of the wheel, a frictionless groove gives the same result.

How? How does it give the same result as an axle which has friction, if we neglect KE of the wheel?

 

[mfb]

The pulley will not dissipate any energy, and the magnitude of force is the same everywhere in the rope.
That is true for every ideal, frictionless pulley, it does not even depend on the details how you design the pulley.

 

[haruspex]

How? How does it give the same result as an axle which has friction, if we neglect KE of the wheel?

That's not what mfb wrote. mfb said that (frictionless axle with massless wheel) gives the same result (i.e. no role in the equations) as frictionless groove.