A student sits on a freely rotating stool holding two dumbbells, each of mass 3.

Question

A student sits on a freely rotating stool holding two dumbbells, each of mass 3.09 kg (see figure below). When his arms are extended horizontally (figure a), the dumbbells are 0.93 m from the axis of rotation and the student rotates with an angular speed of 0.740 rad/s. The moment of inertia of the student plus stool is 2.54 kg·m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.292 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 Kbefore Kafter

Explanation / Answer

Here,

a) let the final angular speed is wf

Using conservation of angular momentum

initial angular momentum = final angular momentum

(2.54 + 2 * 3.09 * 0.93^2) * 0.74 = (2.54 + 2 * 3.09 * 0.292^2) * wf

solving for wf

wf = 1.90 rad/s

the final angular speed is 1.90 rad/s

b) for the initial kinetic energy

Kbefore = 0.50 * I * w^2

Kbefore = 0.50 * (2.54 + 2 * 3.09 * 0.93^2) * 0.74^2

Kbefore = 2.16 J

Kafter = 0.50 * I * wf^2

Kafter = 0.50 * (2.54 + 2 * 3.09 * 0.292^2) * 1.90^2

Kafter = 5.53 J

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