A narrow but solid spool of thread has radius RR and mass MM$.$If you pull up on the thread so that the CM of the spool remains suspended in the air at the same place as it unwinds, what force must you exert on the thread?

Express your answer in terms of the variable MM and appropriate constants.How much work have you done by the time the spool turns with angular velocity $?$

Express your answer in terms of the variables MM$,$ RR$,$ and $.$

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