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Question

https://proteus.physics.ndsu.nodak.edu/res/whfreeman/tipler/Physics_for_Scientists_and_Engineers_6e/Chap10/graphics/tipler10-52.gif
Two disks of identical mass but different radii (r and R = 6.50r) are spinning on frictionless bearings at the same angular speed but in opposite directions. The two disks are brought slowly together. The resulting frictional force between the surfaces eventually brings them to a common angular velocity. What is the ratio of the magnitude of the final angular velocity to the initial angular velocity?

Explanation / Answer

as masses are equal for both discs

moment of inertia is proportional to radius^2

using conservation of angular momentum

Initial angular momentum = final angular momentum
(-r^2 + 6.5r^2) = (r^2 + 6.5r^2)'

'/ = (6.5-1 )/(6.5+1) = 5.5/7.5 = .7333

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