Tension is uniform only in the ideal string limit

01
The tempting model
Assuming every connected segment has the same tension even with mass or friction in the connector.
02
Why it feels right
Intro pulley problems train the reflex that one string means one tension.
03
Where it breaks · how to catch it
You set tensions equal across a massive rope, rough pulley, or string wrapped around a post.
04
The correct model
Equal tension requires a massless string over frictionless supports. If the connector has mass or a pulley has rotational inertia/friction, different tensions supply its acceleration or torque.
05
Repair · see it, then test it
worked example A massive rope is pulled upward while accelerating. Is the tension at the top equal to the bottom?
Tempting move
Yes — same rope.
Correct move
No. The top must support and accelerate all rope below it, so tension varies with position.
Test the repair NL-11 · transfer

A pulley has rotational inertia and angular acceleration. How do the string tensions on its two sides compare?
They must be equal because it is one string They differ so their torque difference can accelerate the pulley Both are zero The larger tension is always on the left

Make a fresh prediction before referring to the worked example.
Then practise it on the ladder
R37Pulley with rotational inertiaadds: Different string tensions can create pulley torque.R38Massive pulley Atwood accelerationadds: Rotational inertia modifies the effective mass of a pulley system.