Competitive ice skaters commonly perform single, double, and tripleaxel jumps in

Question

Competitive ice skaters commonly perform single, double, and tripleaxel jumps in which they rotate 1 1/2, 2 1/2, and 3 1/1revolutions, respectively, about a vertical axis whileairborne. For all these jumps, a typical skater remainsairborne for about 0.70 seconds. Suppose a skater leaves theground in an "open" position (e.g. arms outstretched) with momentof inertia I0 and rotational frequency f0 =1.2 rev/s, maintaining this position for 0.10 seconds. Theskater then assumes a "closed" position (arms brought closer) withmoment of inertia I, acquiring a rotational frequency f, which ismaintained for 0.50 seconds. Finally, the skater immediatelyreturns to the "open" position for 0.10 sec untillanding.
(a) why is angular momentum conserved during the skater's jump?neglect air resitance
(b) determine the minimum rotational frequency f during theflight's middle section for the skater to successfully complete asingle and a triple axel.
(c) show that, according to this model, a skater must be ableto reduce his or her moment of inertia in midflight by a factor ofabout 2 and 5 in order to complete a single and triple axel,respectively.

Explanation / Answer

(A) Angular momentum is defined as L = I. Asshe closes her arms, I decreases (her inertia), but this causeshere to spin faster, so increases. Therefore, angularmomentum is conserved.

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