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1. The problem statement, all variables and given/known data

This is Advanced Physics by Adams and Allday, spread 3.31, question 3.

A pirouetting skater halves his moment of inertia by pulling in his arms and legs closer to his axis of rotation.

a) By what factor does his angular velocity increase?

2. Relevant equations

Angular momentum [itex]L = I \omega[/itex]

Rotational kinetic energy [itex]R.K.E. = 0.5 I {\omega}^2[/itex]

3. The attempt at a solution

I think this problem is soluable by either conservation of momentum or conservation of energy but I get different answers using these methods.

Using subscript 1 to denote the skater's initial state and subscript 2 to denote the skater's final state,

by conservation of energy

[tex]L_1 = L_2[/tex]

[tex]I_1 {\omega}_1 = I_2 {\omega}_2 [/tex]

[tex]I_1 {\omega}_1 = 0.5 I_1 {\omega}_2 [/tex]

[tex]\frac {{\omega}_2} {{\omega}_1} = \frac {I_1} {0.5 I_1}[/tex]

[tex]\frac {{\omega}_2} {{\omega}_1} = 2[/tex]

by conservation of energy

[tex]R.K.E._1 = R.K.E._2[/tex]

[tex]0.5 I_1 {\omega_1}^2 = 0.5 I_2 {\omega_2}^2 [/tex]

[tex]I_1 {\omega_1}^2 = (0.5 I_1) {\omega_2}^2 [/tex]

[tex]{\omega_1}^2 = 0.5 {\omega_2}^2 [/tex]

[tex]\frac {{\omega_2}^2} {{\omega_1}^2} = 2[/tex]

[tex]\frac {\omega_2} {\omega_1} = \sqrt{2}[/tex]

What am I doing wrong?

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# Homework Help: Angular velocity - different ans by conserv E and momentum

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