practice exam question A 50 kg student is holding a 2.0 kg mass in each hand and

Question

practice exam question

A 50 kg student is holding a 2.0 kg mass in each hand and is sitting on a stool that can rotate freely about a vertical axis. With the masses held at arm's length the student is set spinning at 1 revolution per second. While spinning, the student draws their arms in, holding the masses to their chest. Using the principles of rotational motion that you learned in PHYS140, explain what happens to their rotation. During this motion, does the student's kinetic energy increase, decrease, or stay the same? Justify your answer.

Explanation / Answer

a)When the students folds his arms and brings the masses closer to himself the moment of inertia of the system decreases but since there is no external torque on the system the angular momentum is constant so too keep the product I* constsnt with decreased I the angular velocity increases( I1>I2)

I11 = I22 => 2 = I1/I2 => 2>1

b) The energy of system is .5i^2

we have for the initial and final condition the ratio of Energy = I11^2/I22^2 = I2/I1

so the energy in the latter case is more as I1>I2

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