Assuming all dancers have the same mass, and AP axis refers to the anteroposterior axis (imaginary axis of rotation running through the chest and back of the dancers):

Catherine has the largest moment of inertia as I=mr^2. Catherine has one of her legs and two of her arms stretched out far from the axis of rotation meaning more of her mass is away from the center of rotation which increases her moment of inertia.

In the longitudinal axis, we have

- Catherine 2. Anna 3. Bryn 4. Donna

Donna has the least moment of inertia along the longitudinal axis because her outstretched arms run along the axis of rotation making r close to 0.

Given they have the same angular velocity, the greatest angular momentum will be that of the dancer with the highest moment of inertia, L=Iw. So, Catherine has the highest momentum.

If we have equal momenta, then the dancer with the greatest velocity will be the one with the least inertia, w=L/I. So, Donna has the greatest velocity.

answered by @juanv2 •
about 1 year ago

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