How Is Angular Speed Calculated for a Pulley System?

AI Thread Summary
Angular speed for a pulley system can be calculated using the relationship v = rω, where v is the linear velocity, r is the radius, and ω is the angular speed. The discussion centers on determining the angular speed of the pulley, particularly in relation to two boxes with a common velocity. The proposed formula for angular speed is ω = (1/R) * √((2gh)(mA - mB)/(mA + mB + I/R²)). Participants confirm that the approach and calculations appear correct, emphasizing the importance of understanding the conservation of energy in this context. Accurate calculations are crucial, especially given the question's high point value.
dennislam
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Homework Statement


problem.png


Homework Equations


v=rω
conservation of energy

The Attempt at a Solution

20161103_145743.jpg


I don't know whether it is correct or not, and I am quite confused in part b
it asks the angular speed of the pulley
can I say that v=rω since the pulley and box A,B have a common velocity?
so is ω equal to 1/R*√((2gh)(mA-mB)/(mA+mB+I/R^2))?
but the question is worth 10 marks:H
 
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dennislam said:

Homework Statement


View attachment 108390

Homework Equations


v=rω
conservation of energy

The Attempt at a Solution

View attachment 108391

I don't know whether it is correct or not, and I am quite confused in part b
it asks the angular speed of the pulley
can I say that v=rω since the pulley and box A,B have a common velocity?
so is ω equal to 1/R*√((2gh)(mA-mB)/(mA+mB+I/R^2))?
but the question is worth 10 marks:H
That all looks right.
 
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