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

  • Thread starter Thread starter urekmazino
  • Start date Start date
  • Tags Tags
    Pulleys
AI Thread Summary
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.
urekmazino
Messages
3
Reaction score
0
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
 
Mathematics news on Phys.org
Use the fact that the length of the belt moved past each pulley in any period of time is the same for both pulleys.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
Back
Top