Engineering How to find the angular velocity of a rotating drum?

AI Thread Summary
To find the angular velocity of a rotating drum, understanding the relationship between linear and angular velocities is crucial. The discussion highlights that the point of contact between the pulley and the rope has zero velocity, which is key to determining the angular velocity. When the pulley falls a unit distance in one second, it prompts questions about the speeds of the ropes at different branches and how they relate to the circumference movement of another pulley. Clarifications on these points lead to a better understanding of the mechanics involved. Overall, the conversation emphasizes the importance of visualizing the system to solve for angular velocity effectively.
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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