Question #295116

Dhabitah, a 60 kg diver is positioned so that her radius of gyration is 0.5 m as she leaves the board with an angular velocity of 4 rads-1. Compute Dhabitah’s angular velocity when she assumes a tuck position, altering her radius of gyration to 0.25 m. Explain how the diver applied the conservation of angular momentum to perform a somersault.



1
Expert's answer
2022-02-13T12:12:49-0500

Answer


Given data are


Mass of diver m=60kg




radius of gyration is K1

0.5 m




an angular velocity of ω1=


1 4 rads-1




Now




radius of gyration is K2=0.25 m




an angular velocity of ω 2


= ?




applied the conservation of angular momentum to perform


I1ω1=I2ω2ω2=I1ω1I2ω2=mK12ω1mK22I_1\omega_1=I_2\omega_2\\\omega_2=\frac{I_1\omega_1}{I_2} \\\omega_2=\frac{mK_1^2\omega_1}{mK_2^2}


So values putting


ω2=(0.5)2×4(0.25)2=16rad/sec.\omega_2=\frac{(0.5)^2\times4}{(0.25)^2}\\=16rad/sec.





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