How to find the angular velocity of a rotating drum?

[Amaelle]

Homework Statement

look at the image below

Relevant Equations

v=w*r
Va=vB+vB/A

Good day
here is the exercice

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!

 

[Lnewqban]

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.

 

[Amaelle]

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?

 

[Frodo]

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.

 

[Lnewqban]

so you mean that the point of contact between pulley 5 and branch A has a zero velocity? (a center of instantaneous rotation?

Exactly!

 

[Amaelle]

thanks a million!

 

[Amaelle]

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 :)

 

[Lnewqban]

thanks a million!

You are welcome.
Please, see:
https://www.physicsforums.com/insights/explaining-rolling-motion/