A student sits on a freely rotating stool holding two weights,each of mass 3.10

Question

A student sits on a freely rotating stool holding two weights,each of mass 3.10 kg. When his armsare extended horizontally, the weights are 0.92 m from the axis of rotation and he rotateswith an angular speed of 0.747 rad/s.The moment of inertia of the student plus stool is 3.10 kg·m2 and is assumed to beconstant. The student pulls the weights inward horizontally to aposition 0.305 m from the rotationaxis. (a) Find the new angular speed of the student.
1 rad/s

(b) Find the kinetic energy of the rotating system before and afterhe pulls the weights inward.
2 J (before)
3 J (after) A student sits on a freely rotating stool holding two weights,each of mass 3.10 kg. When his armsare extended horizontally, the weights are 0.92 m from the axis of rotation and he rotateswith an angular speed of 0.747 rad/s.The moment of inertia of the student plus stool is 3.10 kg·m2 and is assumed to beconstant. The student pulls the weights inward horizontally to aposition 0.305 m from the rotationaxis. (a) Find the new angular speed of the student.
1 rad/s

(b) Find the kinetic energy of the rotating system before and afterhe pulls the weights inward.
2 J (before)
3 J (after)

Explanation / Answer

By the rotational conservation of momentum I00 =Iff                             (1) where is the angular speed before and after the studentpulls the weights inwards;   I, is the total momentum ofinertia, including stool, student, and the 2 weights: I0 = Is +2mr02 If = Is + 2mrf2 where Is = 3.10 kgm2, m = 3.10 kg, r0 =0.92 m, rf = 0.305 m where Is = 3.10 kgm2, m = 3.10 kg, r0 =0.92 m, rf = 0.305 m . Substituing in equation (1) f = (Is +2mr02)0 /(  Is + 2mrf2) f = (2.27039)(0.747 rad/sec) f = 1.695 rad/sec B) To solve this, use the rotational equation for the kineticenergy K = (1/2) I2 Then K0 = (1/2)I002 K0 = 0.5(8.34768)(0.747)2 K0 = 2.3290 J K0 = 2.3290 J Kf = (1/2)Iff2 Kf = 0.5(3.6767)(1.695)2 Kf = 5.28170 J Kf = 0.5(3.6767)(1.695)2 Kf = 5.28170 J

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