A student sits on a rotating stool holding two 3.0 kg objects. When his arms are

Question

A student sits on a rotating stool holding two 3.0 kg objects. When his arms are extendedhorizontally, the objects are 1.0 m from the axis of rotation, andhe rotates with an angular speed of 0.75 rad/s. The moment ofinertia of the student plus stool is 3.0 kg·m2and is assumed to be constant. The student then pulls the objectshorizontally to 0.40 m from therotation axis. (a) Find the new angular speed of thestudent.
1 rad/s

(b) Find the kinetic energy of the student system before and afterthe objects are pulled in. before 2 J after 3 J (a) Find the new angular speed of thestudent.
1 rad/s

(b) Find the kinetic energy of the student system before and afterthe objects are pulled in. before 2 J after 3 J before 2 J after 3 J

Explanation / Answer

(a)
   from the given problem the total anguar momentum ofthe system of the student the stool and the
   weights about the axis of rotation is givenby
   Itotal = Iweights +Istudent   
           = 2 (m r2) + 3.07 kg . m2
   intially we get
   r = 0.98 m
   Ii = 2 (3.0 kg) (0.98 m)2 + 3.0kg . m2
      = ........ kg . m2
   finally
   r = 1.0 m
   If = 2 (3.0 kg) (1.0 m)2 + 3.0kg . m2
       = ........ kg .m2
   according to the law of conservation of momentum weget
   If f = Iii
   solve for f
   f = ........ rad / s
(b)
   KEi = (1 / 2) Iii2
          = ........J
   KEf = (1 / 2) Iff2
          = ........J

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