$A$ small particle of mass $m$ is given an initial high velocity in the horizontal plane and winds its cord around the fixed vertical shaft of radius $a$. All motion occurs essentially in the horizontal plane. If the angular velocity of the cord is $\omega_0$ when the distance from the particle to the tangency point is $r_0$,then the angular velocity of the cord $\omega$ after it has turned through an angle $\theta$ is

• A
  $\omega = \omega_0$
• B
  $\omega = \frac{a\omega_0}{r_0}$
• C
  $\omega = \frac{\omega_0}{1 - \frac{a\theta}{r_0}}$
• D
  $\omega = \omega_0\theta$