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A small blob of putty of mass m falls from the ceiling andlands on the outer rim

ID: 1725773 • Letter: A

Question

A small blob of putty of mass m falls from the ceiling andlands on the outer rim of a turntable of radius R andmoment of inertia I0 that is rotating freelywith angular speed 0 about its verticalfixed-symmetry axis. (Use the following variables as necessary:omega_0 for 0, I_0 forI0, m, and R.)

(a) What is the postcollision angular speed of theturntable-putty system?

(b) After several turns, the blob flies off the edge of theturntable. What is the angular speed of the turntable after theblob's departure?

Explanation / Answer

          Given thatthe moment of inertia of turntable is Io           Radius oftable is R           mass ofputty is m           initialangular velocity is o ----------------------------------------------------------------------    Since there is no external torque on the system so theangular momentum conserved               Total initial angular momentum = total final angular momentum                                 Io*o = ( Io + mR2)                                                           = Io*o / ( Io + mR2)                                                              (b) If the blob flies off tangentially to the turntable, itsangular momentum doesn’t change (with respect to an axisthrough the center of turntable). Because there is no external torqueacting on the blob-turntable system, the total angular momentum of the system will remain constant and the angularmomentum of the turntable will not change.                                   So final angular velocity is only