Answer to Question #295141 in Mechanics | Relativity for zati

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

Mass of diver m=60kg

radius of gyration is K₁=0.5 m

an angular velocity of $\omega_1=$ 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 a somersault

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

Putting all values

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