Hello, I am wondering if someone can answer me this question: In an Atwood machine why do the tensions that handle both bodies are the same? (English is not my native language)

Answer 1

well, assuming that the string exerts no torque on the wheel and that the string is of zero mass, there is nothing to change the tension in the string as it runs over the wheel.

(In real life of course the wheel has mass and moment of inertia and the difference in tension on each side of the wheel accelerates the spin of the wheel. However this effect is assumed small because both the friction and moment of inertia of the wheel are considered small)