Observed angular velocity function of object moving in straight path

[bendloewen]

Hello, I have been trying to find an equation to represent the observed angular velocity of any object traveling in a straight path x and y distance away from where its being observed, along with the moving objects velocity. My problem is that I am getting a differential equation that in its simplest terms makes complete sense, but I can't get anything out of it. If you all could help out that would be great. I have attached an illustration, with my progress on it so far in the upper right corner. I am needing this for a camera tracking system, where it sees points as x and y coordinates. After calibrated, I need to include its observed angular velocity, and I could include angular acceleration that would be great too! Thanks again for all of your help.

 

[Chestermiller]

Hello, I have been trying to find an equation to represent the observed angular velocity of any object traveling in a straight path x and y distance away from where its being observed, along with the moving objects velocity. My problem is that I am getting a differential equation that in its simplest terms makes complete sense, but I can't get anything out of it. If you all could help out that would be great. I have attached an illustration, with my progress on it so far in the upper right corner. I am needing this for a camera tracking system, where it sees points as x and y coordinates. After calibrated, I need to include its observed angular velocity, and I could include angular acceleration that would be great too! Thanks again for all of your help.

x = y tanθ

$$\frac{dx}{dt}=y sec^2θ\frac{dθ}{dt}$$
$$sec^2θ=\frac{x^2+y^2}{y^2}$$

 

[bendloewen]

Thankyou for the answer, could you tell us where you got the sec^2=x^2+y^2/y^2? I have never seen that in any of my maths

 

[bendloewen]

nevermind i just figured it out haha. Thanks!

 

[blue_raver22]

I would suggest using the formula ω = v/r, where ω is the angular velocity, v is the linear velocity, and r is the distance from the center of rotation. This formula applies to objects moving in a circular path, but can also be used for objects moving in a straight path as long as the distance from the center of rotation is constant. If the distance is changing, you may need to use the formula ω = v/√(x^2+y^2), where x and y are the distances from the center of rotation at each point in time. Additionally, if you want to include angular acceleration, you can use the formula α = a/r, where α is the angular acceleration and a is the linear acceleration. I hope this helps with your camera tracking system. Good luck!