A wheel of moment of inertia $\mathrm{{\rm I}}$ and radius R is rotating about its axis at an angular speed ${\mathrm{\omega }}_0.$  A small fragment of mass m breaks off from its rim. Find the final angular velocity of the wheel.

• A

  $\frac{\mathrm{I}{\mathrm{\omega }}_0}{\left(\mathrm{I}-{\mathrm{mR}}^2\right)}$

• B

  ${\mathrm{\omega }}_0$

• C

  $\frac{\mathrm{I}{\mathrm{\omega }}_0}{\left(\mathrm{I}+{\mathrm{mR}}^2\right)}$

• D

  $\frac{\left(\mathrm{I}+{\mathrm{mR}}^2\right){\mathrm{\omega }}_0}{\mathrm{I}}$