Common angular speed after collision

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The discussion revolves around calculating the common angular speed of two disks after a collision. Disk A, with a mass of 9.0 kg and a radius of 90 cm, rotates clockwise at 30 rev/s, while Disk B, also 9.0 kg but with a radius of 10 cm, rotates counterclockwise at the same speed before landing on Disk A. The conservation of angular momentum is highlighted as the key principle to solve the problem. Initial calculations of angular momentum for both disks are presented, but the user struggles with the final computations. Ultimately, the common angular speed after the collision is determined to be approximately 29.27 rev/s.
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Homework Statement



Disk A, with a mass of 9.0 and a radius of 90 , rotates clockwise about a frictionless vertical axle at 30 . Disk B, also 9.0 but with a radius of 10 , rotates counterclockwise about that same axle, but at a greater height than disk A, at 30 . Disk B slides down the axle until it lands on top of disk A, after which they rotate together.

Homework Equations



ive been trying to find the acceleration? a=delta w/delta t but obviously this isn't wokring!

The Attempt at a Solution


I can't even attempt a solution. I am completely lost on this one, so much so i registered for physics forum just to get some help.
 
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Whats the question? Edit: I see it now in the heading. What about conservation of angular momenta?
 
the setup: disk a has a mass of 9.0 kg and a radius of 90cm, rotates clockwise about a frictionless vertical axle at 30 rev/s. disk b, also 9.0 kg but with a radius of 10cm rotates counterclockwise about that same axle but at a greater height than disk a, at 30 rev/s. disk b slides down the axle until it lands on top of disk a, after which they rotate together. after the collision, what is their common angular speed in rev/s?

i tried:
A has L= I x w, I = mass x rad^2 = 7.29 x -30 = -218.7 L for b = +2.7. So the final L = -216 CW

its not working. very frustrating.
 
maybe the math--using cm-kg: this is the (1/2 mR^2) x revs/sec
a: +9 x 8100/2 x 30
b: -9 x 100/2 x 30
Sum: 9 x 8000/2 x 30 = 36000 x 30 = 108 x 10^4

Sum for the composite= [9 x 8100/2 + 9 x 100/2] x ? =9 x 4100 x ?
? = 29.27 RPS

PS: clockwise rotation I define as positive quantity.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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