Analysis of a wind vane/weather vane

Hi



I am trying to create a model to simulate the motion of a weather vane. It basically looks at the wind direction and as the wind direction changes, the objects responds by trying to align itself parallel to the wind.



First of all I am looking at the force perpendicular to the pivot point of the vane. This force increases as there is a greater change in the wind direction.



I am using F= 0.5*rho*(v^2)*A to calculate the force

where v = velocity (wind speed) and A=area of the vane



I am using this force and resolving it for an angle (theta) which is the change of wind direction. I am then calculating the turning moment of the object by using this resolved force and the distance from the pivot point. This turning moment governs the respond of the object to the change in the wind direction.



I am stuck right now because I need to try and incorporate the mass of the object in this model. I am not sure where is the right place to include this and what equation do I need to use?



Can you please help/guide me in the right direction?



Thank you