A student sits on a stool that is free to rotate about a vertical axis. The stud

Question

A student sits on a stool that is free to rotate about a vertical axis. The student holds her arms extended horizontally with a 4.0 kg. dumbbell in each hand.

The instructor starts the student rotating with angular speed of 0.50 rev/ sec

Assume also that the rotational inertia o the student remains constant at 5.0 kg m2 as the student pulls her hands to her sides and that the change in rotational inertia is due only to the puling the dumbbells inward.

The original distance of the dumbbells from the axis of rotation starts at 90 centimeters. The final distance becomes 15 centimeters.

Find the final angular speed of the student.

Explanation / Answer

In such situation we can conserve angular momentum.

I1 x w1 = I2 x w2

(5 + 2 x 4 x 0.9^2) x 0.5 = ( 5 + 2 x 4 x 0.15^2) x w2

w2 = 1.108 rev/s

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