Answer to Question #295135 in Mechanics | Relativity for leonardo

Question

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. 

Answer 1

Answer

Given data are

Mass of diver m=60kg

radius of gyration is K$_1$ =0.5 m

an angular velocity of$\omega_1=$

1 4 rads-1

Now

radius of gyration is K₂=0.25 m

an angular velocity of$\omega_2$ = ?

applied the conservation of angular momentum to perform

$I_1\omega_1=I_2\omega_2\\\omega_2=\frac{I_1\omega_1}{I_2} \\\omega_2=\frac{mK_1^2\omega_1}{mK_2^2}$

So putting all values

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