Question

Good evening friends,
solve it plzz.......​

Answer 1

Answer:

Given:

Ballet dancer is rotating at 90 rpm. Now she folds the arm , the moment of Inertia about the same axis of rotation becomes changed to 75% .

To find:

New Angular Velocity

Concept:

As their is no external torque on the system , the angular momentum of the system remains constant.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \huge{ \blue{ \tau = 0}}}$

So, Angular Momentum = constant :

$\therefore L = constant \\ </p><p> \implies \: i \times \omega = constant$

Where I => Moment of Inertia, ω => Angular Velocity.

Calculation:

$\therefore \: I_{1} \times \omega_{1}=I_{2} \times \omega_{2}$

$\implies I_{1} \times 90= (\dfrac{75}{100} I_{1}) \times \omega_{2}$

$\implies I_{1} \times 90= (\dfrac{3}{4} I_{1}) \times \omega_{2}$

$\implies \omega_{2} = 90 \times \dfrac{4}{3}$

$\implies \omega_{2} = 120 \: rpm$

So final answer :

$\: \: \: \boxed{ \red{ \sf{ \huge{ \omega_{2} = 120 \: rpm}}}}$