1. A physics student is sitting on a frictionless platform that is rotating with
ID: 1291684 • Letter: 1
Question
1. A physics student is sitting on a frictionless platform that is rotating with an angular speed of wi = 3.8 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 = 13.2 kg*m2. When the student pulls the weights inward toward his body, the moment of inertia decreases to If = 6.0 kg*m2. What is the resulting angular speed, wf, of the platform?
2. By how much is the kinetic energy of the system increased? (Think about where this increase in energy comes from!)
Explanation / Answer
Given thatthe initial angular speed of the system is ?i = 3.8rad/s
The moment ofinertia of the student, the extended weights, and the platformabout the rotation axis is Ii = 13.2kg*m2.
Thefinal moment of inertia is If = 6.0kg*m2.
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since there is no external torque or force on the system then theangular momentum is conserved
Li = Lf
Ii*?i = If*?f
?f = Ii*?i /If
= 8.36 rad/s
The increasing inthe kinetic energy is ?K = Kf - ki
=(1/2)If?f2 -(1/2)Ii?i2
= 114.36 J
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