Question

A rod of mass 'M' and length 'L' is placed on frictionless horizontal surface. Rod is given an angular velocity ${\omega }_0$ as shown in figure. When rod rotates by ${90}^{\circ }$, it hits a stationary hinge and gets attached to it. New angular velocity is $\omega$ such that $\omega =n{\omega }_0$. Here n is . (Answer upto two digits after the decimal point.)

Answer 1

By, conservation of angular momentum about the hinge
$\Rightarrow L_i=L_f$

$\frac{M{L}^2}{12}{\omega }_0=\frac{M{L}^2}{3}\omega \Rightarrow \omega =\frac{{\omega }_0}{4}=0.25{\omega }_0$
$\Rightarrow n=0.25$