Two disks of identical mass but different radii ( r and 2 r ) are spinning on fr

Question

Two disks of identical mass but different radii (r and 2r) are spinning on frictionless bearings at the same angular speed 0, but in opposite directions as shown in the figure. The two disks are brought slowly together. The resulting frictional force between the surfaces eventually brings them to a common angular velocity. What is that final angular velocity (magnitude and direction) in terms of 0? By our typical sign convention, the smaller disk has a positive angular velocity originally.

A. -3/5 0

B. 0

C. -140

D. -120

E. 140

Explanation / Answer

Principle of conservation of angular momentum

We invoke the conservation of angular momentum p = iW and P = IW where i = mr^2 and I = m4r^2 and W are the same angular speeds.

So we have p + P = (i + I)w = iW - IW; so w = W (i - I)/(i + I) = W (1 - 4)/(1 + 4) = - 3/5 W

ANS is option (a) where W = your 0. Note the negative W showing opposite direction to W.

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