Two  particles move on  a circular  path (one just  inside  and the other  just outside the circle) with  angular  velocities   $\omega and5\omega$ starting  from the  same position .They  cross  each other

At intervals of time $\frac{\pi }{4\omega }$ if  their  angular  velocities  are in the same  sense

At successive  points  on the  path  subtending  an angle  of$\text{6}0°\text{C}$ at the center  if their angular  velocities   are opposite  directed 

At  intervals  of  time $\frac{\pi }{3\omega }$if their  angular  velocities  are oppositely  directed 

At successive  points  on the path  subtending  an angle  of $45°C$ at the center if  their  angular velocities are oppositely  directed