A disk with moment of inertia $$I1$$ rotates about a frictionless, vertical axle with angular speed ωi. A second disk, this one having moment of inertia $$I2$$ and initially not rotating, drops onto the first disk (Fig$$.$$). Because of friction between the surfaces, the two eventually reach the same angular speed ωf The value of ωf is

Question

A disk with moment of inertia $$I1$$ rotates about a frictionless, vertical axle with angular speed ωi.  A second disk, this one having moment of inertia $$I2$$ and initially not rotating, drops onto the first disk (Fig$$.$$). Because of friction between the surfaces, the two eventually reach the same angular speed ωf The value of ωf is

Infinity Learn · Accepted Answer

From conservation of angular momentum for the isolated system of two disks:(I1+I2)ωf $$=$$ $$I1$$ωi or ωf $$=$$ $$I1I1+I2$$ωi

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