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When a diver gets into a tuck position by pulling in her arms and legs, she increases her angular speed. Before she goes into the tuck position, her angular velocity is 5.5 rad/s, and she has a moment of inertia of 2.1 kg · m2. Once she gets into the tuck position, her angular speed is 12.9 rad/s. Determine her moment of inertia, in kg · m2, when she is in the tuck position. Assume the net torque on her is zero.

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Answer:

0.89534 kgm²

Explanation:

[tex]\omega_f[/tex] = Final angular velocity = 12.9 rad/s

[tex]\omega_i[/tex] = Initial angular velocity = 5.5 rad/s

[tex]I_i[/tex] = Initial moment of inertia = 2.1 kgm²

[tex]I_f[/tex] = Final moment of inertia

As there is no external torque the angular momentum is conserved

[tex]I_i\omega_i=I_f\omega_f\\\Rightarrow I_f=\dfrac{I_i\omega_i}{\omega_f}\\\Rightarrow I_f=\dfrac{2.1\times 5.5}{12.9}\\\Rightarrow I_f=0.89534\ kgm^2[/tex]

The final moment of inertia is 0.89534 kgm²

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