# A ballerina spinning at 1.2 rev/sec with a moment of inertia of 2.6 kgm2 pulls her arms in so that her new moment of inertia is 1.8 kgm2. What is her new angular speed?

$10 , 891 r a d / s$
${L}_{1} = {L}_{2}$
$\therefore {I}_{1} {\omega}_{1} = {I}_{2} {\omega}_{2}$
$\therefore {\omega}_{2} = \frac{{I}_{1} {\omega}_{1}}{{I}_{2}} = \frac{\left(2 , 6 k g . {m}^{2}\right) \left(7 , 54 r a d / s\right)}{1 , 8 k g . {m}^{2}} = 10 , 891 r a d / s$