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 3.0 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
(b) Find the kinetic energy of the student before and after theobjects are pulled in.
2


(a) Find the new angular speed of thestudent.
1
(b) Find the kinetic energy of the student before and after theobjects are pulled in.
2



2

Explanation / Answer

mass m = 4 kg distance of the object from the axis x = 1 m angular speed w = 0.75 rad / s moment of inertia of the student plus stool I = 3kg m ^ 2 Final moment of inetia I ' = I - m ( 1 - 0.4 ) ^ 2                                        =3 - 4 ( 0.6 ) ^ 2                                       = 1.56 kg m ^ 2 from law of conservation of angular momentum , I w = I 'w ' from this new angular speed w ' = Iw / I '                                                 = 1.442 rad / s Kinetic energy before pulled = ( 1/ 2) I w ^ 2 Kinetic energy after pulled = ( 1/. 2) I ' w ' ^ 2

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