Conservation of momentum/energy

[henry3369]

Homework Statement

http://imgur.com/cEqXb24

Homework Equations

Ki = Kf
Li = Lf

The Attempt at a Solution

So I tried to solve this using conservation of energy as well as conservation of momentum, but only conservation of momentum gave the correct answer. Why can't conservation of energy be used in this situation?

 

[henry3369]

Here is the work:
Both of these moments of inertia already include the body:
I_initial = 2.83
I_final = 0.9625
ω_initial = 0.40 rev/s

Using conservation of momentum:
I_initialω_initial = I_finalω_final
(2.83)(0.4) = (0.9625)ω_final
ω_final = 1.2 rev/s

Using conservation of energy:
W_{non-conservative forces} = 0 and no potential energy.
K_initial = K_final
(1/2)I_initialω_initial² = (1/2)I_finalω_final²
(2.83)(0.40²) = (0.9625)(ω_final²)
ω_final = 0.69 rev/s

 

[henry3369]

Also, if there were a non conservative force such as friction, momentum would not be conserved because it would be an external force.

 

[DrClaude]

The skater has to do work to bring the arms closer to the body, and this increases the kinetic energy.