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 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

Initial moment of inertia is that of the student & stoolplus the two masses:   Ii = 3.0 + 4.0x1.02 + 4.0x1.02 = 11.0 kgm2 Final moment of inertia is same idea, but the masses arecloser:   If = 3.0 + 4.0x0.402 + 4.0x0.402 =  4.28 kgm2 Now, since angular momentum is conserved:    Ii i =   If f         11.0 x 0.75   = 4.28 x      or   final = 1.93 rad/s initial KE = (1/2) I 2 = (1/2)  x 11.0  x 0.752 =3.09 J final KE = (1/2) I 2 = (1/2)  x  4.28  x1.932 = 7.97 J Now, since angular momentum is conserved:    Ii i =   If f         11.0 x 0.75   = 4.28 x      or   final = 1.93 rad/s initial KE = (1/2) I 2 = (1/2)  x 11.0  x 0.752 =3.09 J final KE = (1/2) I 2 = (1/2)  x  4.28  x1.932 = 7.97 J

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