Tension is uniform only in the ideal string limit

The mistake

Assuming every connected segment has the same tension even with mass or friction in the connector.

Why it feels right

Intro pulley problems train the reflex that one string means one tension.

How to catch it

You set tensions equal across a massive rope, rough pulley, or string wrapped around a post.

The first principle

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.

worked mini-example

A massive rope is pulled upward while accelerating. Is the tension at the top equal to the bottom?

Common wrong move

Yes — same rope.

Correct

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.