$A$ particle of mass $m$ moves with a velocity $v$ along the rim of a disc of radius $R$ in the counter-clockwise direction. The disc has a moment of inertia $I$ and is rotating in the clockwise direction with an angular velocity $\omega$. If the particle stops moving,what will be the angular velocity of the disc?

• A
  $\frac{I\omega + mvR}{I - mR^2}$
• B
  $\frac{I\omega + mv}{I + mR}$
• C
  $\frac{I^2\omega - m^2vR}{I + mR}$
• D
  $\frac{I\omega - mvR}{I + mR^2}$