A student sits on a rotating stool holding two 4.0 kg objects. When his arms are

Question

A student sits on a rotating stool holding two 4.0 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 beconstant. The student then pulls the objects horizontally to0.40 m from the rotation 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

             Given that the mass of two objects is m = 4.0 kg              Initial distance between the mass and axis of rotation is d1 = 1.0m               Initialangular velocity is 1 = 0.75 rad/s               momentof inertia of stool + student is I = 3.0 kg.m2                 Initialdistance between the mass and axis of rotation is d2 = 1.0m               --------------------------------------------------------------------------           Since there is no external force on the system then the angularmomentum is conserved                             initial angular momentum = final angular momentum                                       (I + 2md12 )1 =   (I + 2md22 )2                            Then                      2 = ( I + 2md12 )1/ ( I +2md22 )                                                                = ---------- rad/s      The kinetic energy before collsion isK1 = (1/2)( I + 2md12)12                                                                   =------------ J      The kinetic energy beforecollsion is K2 = (1/2)( I + 2md22)22                                                                   =------------ J                                                                              =------------ J      The kinetic energy beforecollsion is K2 = (1/2)( I + 2md22)22                                                                   =------------ J                                                                              =------------ J      

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