How to find the angular velocity of a rotating drum?

In summary, the conversation discusses the difficulty in finding the angular velocity of pulley 5. The person suggests imagining the pulley as a wheel and the string as a road to better understand the concept. The point of contact between pulley 5 and branch A is also discussed as having a zero velocity, and the person provides a helpful link for further explanation. The conversation also includes questions about the speed of the rope and the circumference of pulley 3. The final response thanks the person for their help and confirms understanding.
  • #1
Amaelle
310
54
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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  • #2
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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  • #3
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?
 
  • #4
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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  • #5
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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  • #6
thanks a million!
 
  • #7
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 :)
 

1. How do I calculate the angular velocity of a rotating drum?

The angular velocity of a rotating drum can be calculated by dividing the angular displacement by the time it takes to complete one rotation. This can be represented by the formula ω = Δθ/Δt, where ω is the angular velocity, Δθ is the change in angular displacement, and Δt is the time taken.

2. What is the unit of measurement for angular velocity?

The unit of measurement for angular velocity is radians per second (rad/s). This is because angular velocity is a measure of how quickly an object is rotating, and radians are a unit of measurement for angles.

3. How does the mass of the drum affect its angular velocity?

The mass of the drum does not directly affect its angular velocity. However, the distribution of mass within the drum can affect its moment of inertia, which is a factor in the calculation of angular velocity. A drum with a larger moment of inertia will have a lower angular velocity for a given amount of torque applied.

4. Can the angular velocity of a rotating drum change over time?

Yes, the angular velocity of a rotating drum can change over time. This can happen if there is a change in the applied torque, the distribution of mass within the drum, or the surface on which the drum is rotating. Changes in angular velocity can also occur due to external forces such as friction or air resistance.

5. How is angular velocity different from linear velocity?

Angular velocity and linear velocity are two different measures of an object's speed. Angular velocity is a measure of how quickly an object is rotating, while linear velocity is a measure of how quickly an object is moving in a straight line. Angular velocity is typically measured in radians per second, while linear velocity is measured in meters per second.

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