An ice skater is rotating on the tip of one ice skate. At first, her hands are e

Question

An ice skater is rotating on the tip of one ice skate. At first, her hands are extended and she has a moment of inertia of I0; she is rotating at a rate of two turns per second. Then she raises her hands over her head and decreases her moment of inertia to half of its initial value. You can neglect all external forces acting on the skater.

(a) Decide if you should use angular momentum principles or energy principles to determine her final speed of rotation. Be prepared to explain your reasoning.

(b) How fast is she rotating (turns per second) after she raises her hands?

(c) Did her rotational kinetic energy increase, decrease, or stay the same?

(d) If her rotational kinetic energy changed, where did the energy come from (or go to)?

Explanation / Answer

Here ,

initial angular speed , wi = 2 rev/min

inital moment of inertia , I1 = Io

final moment of inertia , I2 = Io/2

a)

as there is no external torque acting on the ice skator

we will use conservation of angular momentum

b)

I1 * w1 = I2 * w2

Io * 2 = Io/2 * w2

w2 = 4 rev/s

she is rotating now with 4 turns per sec

c)

Initial KE = 0.5 * Io * 2^2 = 2 * Io

finla KE = ( 0.5 * Io/2 * 4^2) = 4 * Io

the rotatioanl kinetic energy will increase

d)

the energy comes from the energy in the muscles of the skater

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