Question

A ballet dancer is rotating at an angular velocity $\omega$ on smooth horizontal floor. The ballet dancer folds his body close to his axis of rotation by which his radius of gyration decreases by $\frac{1}{4}$ th of his initial radius of gyration. His final angular velocity is:

• A. $\frac{3\omega }{4}$
• B. $\frac{9\omega }{4}$
• C. $\frac{9\omega }{16}$
• D. $\frac{16\omega }{9}$

Answer 1

The correct option is D $\frac{16\omega }{9}$

$Conservingangularmomentum{I}_1\omega =I_2{\omega }^{\prime }\Rightarrow m{K}_1^2\omega =m{K}_2^2{\omega }^{\prime }{K}_1^2\omega ={\left(\frac{3K_1}{4}\right)}^2{\omega }^{\prime }\Rightarrow {\omega }^{\prime }=\frac{16}{9}\omega$