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 0.20 m from the rotationaxis.(a) Find the new angular speed of the student.
1 rad/s
(b) Find the kinetic energy of the student before and after theobjects are pulled in. before 2 J after 3 J before 2 J after 3 J

Explanation / Answer

The moment of inertia of the student plus stool I = 3.0 kg·m2 mass m = 3 kg distance r = 1 m Initial total moment of inertia I ' = I + m r ^ 2                                         = 3 + ( 3 * 1 ^ 2 ) = 6 kg m ^ 2 Angular speed w ' = 0.75 rad / s New moment of inertia I " = I + m r ' ^ 2                                         = 3 + ( 3 * 0.2 ^ 2 )                                          =3 + 0.12 = 3.12 kg m ^ 2 (a). from law of conservation of angular momentum I ' w' = I " w " new angular speed w " = I ' w ' / I "                                   = 1.442 rad / s (b). the kinetic energy of the student before the objectsare pulled in = ( 1/ 2) I ' w ' ^ 2                                                                                                       = 1.6875 J the kinetic energy of the student after the objects arepulled in = ( 1/ 2) I " w " ^ 2                                                                                                =3.243 J

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