How Is Angular Speed Calculated for a Pulley System?

[dennislam]

Homework Statement

Homework Equations

v=rω
conservation of energy

The Attempt at a Solution

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

 

[haruspex]

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

That all looks right.