Question

The assembly of two discs as shown in figure is placed on a rough horizontal surface and the front disc is given an initial angular velocity ${\omega }_0$ Determine the final linear and angular velocity when both the discs start rolling. It is given that friction is sufficient 10 sustain rolling in the rear wheel from the starting of motion.

Answer 1

$L_i=L_f$ (about bottommost point)
$\therefore I{\omega }_0=2[I\omega +mRv]$ or
$\left(\frac{1}{2}m{R}^2\right){\omega }_0=2[\frac{1}{2}m{R}^2\omega +mR(\omega R\left)\right]$
$\therefore \omega =\frac{{\omega }_0}{6}$ and
$v=\omega R=\frac{{\omega }_{0}R}{6}$