MHB How to Prove the Ratio of Radii and Angular Speeds of Two Connected Pulleys?

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To prove the ratio of radii and angular speeds of two connected pulleys, it is essential to understand that the length of the belt moved past each pulley remains constant over time. Given two pulleys with radii r1 and r2 rotating at angular speeds w1 and w2, the relationship can be established using the formula r1/r2 = w2/w1. This is derived from the fact that the linear speed of the belt is equal for both pulleys, leading to the conclusion that the ratio of the radii corresponds to the inverse ratio of their angular speeds. The absence of specific numerical values does not hinder the proof, as the relationship is purely algebraic. This fundamental principle is crucial for solving problems involving connected pulleys in mechanics.
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Hello there, i need some help on my homework. there's no given numbers that's why it's hard for me to answer this one.

Two pulleys with radii r1 and r2 rotate at angular speeds of w1 and w2. if the pulleys are connected by a belt, show that r1/r2=w2/w1
 
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Use the fact that the length of the belt moved past each pulley in any period of time is the same for both pulleys.
 

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