Froom where did the extra KE came from? You are rotating on a frictionless platf
ID: 1364697 • Letter: F
Question
Froom where did the extra KE came from?
You are rotating on a frictionless platform, holding weights with your arms extended. (The weights are not necessary, they just make it easier to visual what is happening.) As you bring in your arms, your rotation increases due to conservation of angular momentum. Although angular momentum remains constant, a careful examination would show that your rotational KE increases! (And decreases when you extend your arms again.) From where did the extra KE come? Be specific in your explanation.Explanation / Answer
In this case angular momentum of system remains conserved as there is no external torque acting on the system.
Angular momentum = I w where I is moment of inertia and w = angular velocity
When arms are brought inwards then I decreases. For angular momentum to remain constant, w increases, hence person starts rotating fast. There is increase in rotational kinetic energy.
To bring the arms inwards( to decrease moment of inertia), person has done some work. This work done by the person is equal to increase in rotational kinetic energy.
Hence we can conclude that increase in rotational kinetic energy is due to work done by person to decrease his moment of inertia.
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