Question

. Kristen is spinning on the ice at 30 rad/s about her longitudinal axis when she...

. Kristen is spinning on the ice at 30 rad/s about her longitudinal axis when she abducts her arms and doubles her radius of gyration about her longitudinal axis from 32 cm to 64 cm. If her angular momentum is conserved, what is her angular velocity about her longitudinal axis after she increases her radius of gyration (in rad/s)?

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Answer #1

Remember a point mass, m, rotatng at a distance r from an axis, has a moment of inertia = mr² about the axis.

Call Kristen's mass m

If the initial radius of gyration is 32cm (0.32m) this means the initial moment of inertia (I1) is the *same* as a single point mass, m rotating around the axis at r=0.32m.

So I1 = m(0.32)²

So initial angular momentum is

= m(0.32)² * 30  

Similarly, final angular momentum is L2 = m(0.64)² ?2

Since these are equal:
m(0.32)² * 30 = m(0.64)² ?2
?2 = 30 * (0.32/0.64)²
= 7.5 rad/s

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