Question

The angular velocity of a body changes from one revolution per $9$ seconds to $1$ revolution per second without applying any torque the ratio of its radius of gyration in the two cases is.

Answer 1

$I_i=m{r_i}^2$

$I_f=m{r_f}^2$

$W_i=\frac{2\pi }{9}\frac{rad}{sec}$

$W_f=2\pi \frac{rad}{sec}$

$I_i\ast W_i=I_f\ast W_f$

$m{r_i}^2\ast \frac{2\pi }{9}=m{r_f}^2\ast 2\pi$

${\left(\frac{r_i}{r_f}\right)}^2=9$

$\frac{r_i}{r_f}=3$