A student sits on a rotating stool holding two 2.0 kg objects. When his arms are

Question

A student sits on a rotating stool holding two 2.0 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 3.0kg·m2 and is assumed to be constant. Thestudent then pulls the objects horizontally to 0.50 m from the rotation axis. (a) Find the new angular speed of the student.
rad/s

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

(b) Find the kinetic energy of the student system before and afterthe objects are pulled in. before J after J before J after 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) + 3.00 kg . m2
   intially we get
   r = 0.10 m
   Ii = 2 (3.00 kg) (0.10 m)2 +3.00 kg . m2
      = ........ kg . m2
   finally
   r = 0.250 m
   If = 2 (3.00 kg) (0.250 m)2 +3.00 kg . 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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