Step 1: FBD - Draw a free body diagram of the particle P and the bar. Are there any forces creating a moment about point O?
Step 2: Angular momentum - If you did not observe any moments about the fixed point O, then angular momentum about point O is conserved. This will provide you with one equation to find the angular rotation rate of the bar at the second position. How do you find the radial component of velocity, R_dot? [HINT: Energy is also conserved.] This, along with the angular rotation rate of the bar, will give you R_dot.
Step 3: Kinematics - Your kinematics all through the solution will be in terms of the polar components of velocity. Note that the velocity is NOT simply R*omega for the motion of P. Be careful!
Step 4: Solve