A student sits on a freely rotating stool holding two dumbbells, each of mass 2.

Question

A student sits on a freely rotating stool holding two dumbbells, each of mass 2.90 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 1.09 mfrom the axis of rotation and the student rotates with an angular speed of 0.743 rad/s. The moment of inertia of the student plus stool is 2.62 kg · m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.308 m from the rotation axis (Figure b).

(a) Find the new angular speed of the student.
  rad/s

(b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward.

Explanation / Answer

(A)

Angular momentum is conserved

I . w = ( 2.67 + (2 X 2.90 X 1.09^2)) X 0.743 = 7.78 kgm^2/s

I (new) . w(new) = 7.78 = (2.67 + (2 X2.90 X 0.308^2)) . w(new)

w(new) = 2.416 rad/s

b)

K.E = 1/2 . I . w^2 each time.

Before K.E = (0.5) ( 2.67 + (2 X 2.90 X 1.09^2)) X(0.743)2

K.E = (0.5)X(6.89)X(0.552)

K.E = 1.90 joules.

After K.E =(0.5) (2.67 + (2 X2.90 X 0.308^2)) X (0.743)2

K.E = (0.5)X(3.22)X(0.552)

K.E = 0.888 joules.

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