A physics student is sitting on a frictionless platform that is rotating with an

Question

A physics student is sitting on a frictionless platform that is rotating with an angular speed of wi = 3.1 rad/s. His arms are outstretched, and he is holding a heavy weight in each hand. The moment of inertia of the student, the extended weights, and the platform about the rotation axis is Ii = 13.6 kg*m2. When the student pulls the weights inward toward his body, the moment of inertia decreases to If = 5.7 kg*m2.

a) What is the resulting angular speed, wf, of the platform?

b) By how much is the kinetic energy of the system increased? (Think about where this increase in energy comes from!)

Explanation / Answer

Angular momentum is conserved.
Hence:
Ji·i = Jf·f
<=>
f = i·(Ji/Jf)
= 3.1s^-1 · (13.6kg·m² / 5.7kg·m²)
= 7.39s^-1

Change of kinetic energy is:
E = Ef - Ei
= (1/2)·Jf·f² - (1/2)·Ji·i²
= (1/2)·[ Jf·f ² - Ji·i² ]
= (1/2)·[ 5.7kgm² · (7.39s^-1)² - 13.6kgm²·(3.1s^-1)² ]
= 0.0185J

This change in kinetic energy comes from the work done by the student in moving the weight from out to in

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