A shaft whose diameter is d and length i...

A shaft whose diameter is d and length is l is rotating without friction in bearings with an angular velocity `omega_0`. A sleeve of height h and outer diameter `D` is fitted on the shaft (the materials of the sleeve nod the shaft are the same). At first the sleeve is not connected with the shaft and is a t rest. Then at some moment the sleeve is clamped to the shaft. What will be the common angular velocity of the shaft plus the sleeve?

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