How to find the angular velocity of a rotating drum?

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Discussion Overview

The discussion revolves around finding the angular velocity of a rotating drum, specifically focusing on pulley systems and the relationships between linear and angular velocities. Participants explore the mechanics involved in the motion of pulleys and ropes, posing questions and providing hints related to the exercise presented.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses difficulty in determining the angular velocity of pulley 5, given only the linear velocity at its center.
  • Another participant suggests visualizing the problem by comparing the pulley to a wheel and the string to a road surface, implying a relationship between linear and angular motion.
  • There is a discussion about the point of contact between pulley 5 and branch A having zero velocity, which is referred to as a center of instantaneous rotation.
  • Further questions are posed regarding the speeds of the ropes at points A, B, and C, as well as the movement of the circumference of pulley 3 in relation to its angular velocity.
  • Participants confirm understanding of the concepts discussed, with expressions of gratitude for the clarification provided.

Areas of Agreement / Disagreement

Participants generally agree on the mechanics of the problem and the concept of instantaneous rotation, but the discussion remains exploratory without a definitive resolution on the calculations involved.

Contextual Notes

The discussion does not resolve specific mathematical steps or assumptions regarding the relationships between the velocities and angular velocities of the pulleys.

Who May Find This Useful

Individuals interested in mechanics, particularly those studying pulley systems and the relationship between linear and angular velocities, may find this discussion beneficial.

Amaelle
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Homework Statement
look at the image below
Relevant Equations
v=w*r
Va=vB+vB/A
Good day
here is the exercice
exercice pulley.png
The only velocity I do have is the velocity v os the center of pulley 5, I tried to find the center of instantaneous velocity to find the angular velocity of pulley 5 but I couldn't, any hint would be highly appreciated!

Best regards!
 
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Why do you find it difficult?
Imagine the string on the left side of pulley 5 is the surface of a road, that pulley 5 is a wheel, and that v is the velocity of a car.
 
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Lnewqban said:
Why do you find it difficult?
Imagine the string on the left side of pulley 5 is the surface of a road, that pulley 5 is a wheel, and that v is the velocity of a car.
so you mean that the point of contact between pulley 5 and branch A has a zero velocity? (a center of instantaneous rotation?
 
If the pulley 5 falls 1 unit of distance in one second

a) what is the speed of the rope at A?
b) what is the speed of the rope at B?
c) what is the speed of the rope at C?
d) by how much does the circumference of pulley 3 move in one second?

So what is pulley 3's angular velocity? You have the distance the circumference moves in one second.
 
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Amaelle said:
so you mean that the point of contact between pulley 5 and branch A has a zero velocity? (a center of instantaneous rotation?
Exactly!
 
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thanks a million!
 
Frodo said:
If the pulley 5 falls 1 unit of distance in one second

a) what is the speed of the rope at A?
b) what is the speed of the rope at B?
c) what is the speed of the rope at C?
d) by how much does the circumference of pulley 3 move in one second?

So what is pulley 3's angular velocity? You have the distance the circumference moves in one second.
thanks a million, it's clear now :)
 

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