Video Analysis Tutorial and a cat

Cats can be entertaining - especially when they are someone else's cat and that someone made a video. Really, this post is about analyzing video with Logger Pro (in a tutorial type fashion). I just happens that I chose this cat video to analyze. Here is the video:

I am going to look at the part where the cat gets on the fan. I will try to step through the analysis so you can do your own.

Get the video

Actually, the first step is to find a video. YouTube has tons of stuff. Also, you could make your own video with a camera. A couple of things to make your life easier:

• A non-zoom video. If the camera is zooming during the interesting part, you will have to do a lot more work.
• A non-panning video. Again, if the camera stays stationary this is much easier for you.
• Motion of interest is perpendicular to the video camera. Suppose someone was throwing a football. If they threw it right at the camera, the data would be complicated because of the perspective.
• Motion not too close to the camera. Even if the motion is perpendicular, but very close, there will still be perspective issues.
• It is better if the object in motion is at least rigid so that it can mostly be represented by one point. For instance, a person that moves arms and legs around is much more complicated than a ball.
• Finally, a clear shot at the object in motion. If you can't see it the whole time, you can't get data from it the whole time.

Ok. I will assume you have your video. I have mine. What next? Well, if it is on youtube, you need it as a file. There are several ways to get the video from youtube, but I find KickYouTube.com is the most straight forward. Basically, find your youtube video and add the word "kick" in front of youtube.com in the URL. For the cat video, it would look like this:

This new URL will take you to KickYouTube.com where it will give you the options of video formats to download. I would recommend choosing "MP4" as it is the one that will likely give you the least troubles. Also, MP4 should work fine with both Logger Pro and Tracker Video. Click the download button and save your file. Remember where you parked! For this next part, I made a little screen cast using ScreenToaster.

So, from that I have the period of the oscillating fan (at about 1 second). Clearly, there is some error involved here - but I am just getting some rough data. Here is the horizontal position of the cat as a function of time:

I am not really sure what is going on with this data. The data table shows several points with the same time, but it doesn't graph that way. Oh well, good enough. Now for the other piece of data - the angle that the cat swings at. I know that Tracker Video has an angle tool, but Logger Pro does not. I am just going to use a drawing program (I will use KeyNote, but you could use lots of things for this).

For this measurement, I simply drew two lines as a reference. Keynote will give you the angle of a line if you rotate it. I rotated until it looked like it was on the string. This gives an angle of about 28 degrees below the horizontal. Great. I now have the period and the angle. But, what do I want to do with it? Maybe I could calculate the tension in the string. Here is a free body diagram for the cat:

There are only two forces acting on the cat, the tension and the gravitational force. Clearly these two forces do not make a net force of zero. Since the cat is moving in a circle, there needs to be a net force towards the center of the circle. The acceleration of an object moving in a circle is:

Where v is the linear velocity, r is the radius of the circular motion and r-hat is a unit vector pointing outward (thus the negative sign). Perhaps I should post a derivation of this formula sometime. For the case of the cat, I would rather use the angular velocity (although it really doesn't matter). For an object moving in a circle, the linear velocity is related to the angular velocity:

Using this, the magnitude of the circular (centripetal) acceleration is:

In the video, I measured the period of oscillation (usually denoted with a T). So the angular velocity is:

Ok. Now, back to the forces. Newton's law still works, so I can write the following:

Let me call the vertical direction z and the direction towards the center -r. Then I can write Newton's law in its two components:

For the r-direction, the only force is the component of the tension. From above, I will use the angle I found of the rope from the horizontal (call it theta). This gives:

To help keep things a little clearer, I am using T for tension and T_period for the period. Both the force and the acceleration are in the negative r direction (which means towards the center of the circle). Now for the vertical equation.

I hope I didn't confuse you with the vector "g" and the constant g. Oh well. If I want the tension (my original statement) I can use either of these two equations. Both have the mass. What is the mass of a typical cat? According to wikipedia, 2.5 to 7 kg is typical. I will use 5 kg. So, from the vertical equation, I get a tension of:

This is quite a bit larger than if the cat were just hanging (and not spinning - which would be 49 N). Now for the other equation. I can either guess the radius and calculate the tension, or I can calculate what the radius should be. Let me just calculate r.

This seems kind of small, and it is. The reason is that it is wrong. I made the assumption that the string was connected to the rotation point, but it wasn't. The string was connected to the end of the fan. Oh well. I am not going to fix it. The purpose was to show how to do video analysis in Logger Pro. I think I accomplished that.