What does frictionless pulley really mean?

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SUMMARY

The term "frictionless pulley" refers specifically to the axle of the pulley, although neglecting the kinetic energy of the wheel allows for the groove to also be considered frictionless without affecting the outcome. In an ideal frictionless pulley system, energy is not dissipated, and the force remains consistent throughout the rope. This principle applies universally to all ideal frictionless pulleys, regardless of their design specifics. The discussion clarifies that both a frictionless axle with a massless wheel and a frictionless groove yield the same results in mechanical equations.

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When we say "pulley is frictionless", do we mean its groove where the string moves or its axle or both?
 
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The axle - but if you can neglect kinetic energy of the wheel, a frictionless groove gives the same result.
 
mfb said:
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?
 
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.
 
andyrk said:
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.
 

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