 #1
 81
 0
Homework Statement
An Ice skater of mass m = 70kg is initially traveling at a speed v = 4 m/s along a straight path that brings his center of mass to within a distance b = .6m of a vertical pole fixed in the ice. He reaches out with his hand as he passes the pole and hangs on so that he pulls himself into a circular path of radius r = .8m (measured from the axis of rotation to his center of mass) around the pole. If the skater's moment of inertia about his center of mass is I = 1.40 kgm^{2} , what is his final angular velocity ω about the pole, assuming that no torques act during this maneuver?
Homework Equations
L_{i} = L_{f}
I_{i}ω_{i} = I_{f}ω_{f}
or maybe...
L = mvr = Iω
or possibly...
mv_{i}r_{i} = mv_{f}r_{f}
or if energy is conserved...
.5mv^{2} = .5Iω^{2}
I'm mostly confused about which formula to use.
The Attempt at a Solution
mvr_{i} = Iω
(70)(4)(.6) = (1.4)ω
ω = 120 rad/s
But I thought that this was a relatively unreasonable speed for the skater to be going, so I tried this...
.5(70)(4)^{2} = .5(1.4)ω^{2}
ω = 28.3 rad/s
But I don't think energy is conserved, so I also tried this...
mvr = mvr
(70)(4)(.6) = (70)(v)(.8)
v = 2.14 m/s
v=ωr
3 = ω(.8)
ω = 3.75 rad/s
This seemed reasonable to me, but I didn't use the moment of inertia, and I have nothing to check my work against. How do I know which formula is the correct one to use in this situation?
Attachments

16.9 KB Views: 329