Dot Physics

There are several free iPhone-iPod Touch apps that let you look at the acceleration of the device using the built in accelerometer. I was planning on reviewing some of these free apps, but I didn’t. When I started playing around with them, it was clear that I needed some way to make a constant acceleration. There are two simple ways to do this – drop it, or spin it in a circle. I decided to go with the circular motion option because I like my iPod and because Steve Jobs told me to.

While playing with this, I realized that the acceleration depends on the distance of the sensor from the center of the circle of rotation. Where is this sensor? Don’t tell me, I want to figure it out experimentally.

The plan

I am going to spin my iPod in a circle with the “bottom” (you know, where the home button is) towards the center of the circle. I will record the acceleration. I can find the distance to the sensor if I know the angular speed. Next, I will turn the iPod sideways and do it again.

The physics

I am not going to go over all the circular motion stuff – if you want more details, check out this old post on centripetal acceleration. Basically, if something is moving in a circle, it is accelerating because it is changing velocity (even if just the change in direction of that velocity). The direction of this acceleration is towards the center of the circle and it has a magnitude of:

i-6ace7bd208fc7404f3baad6d734f416f-2010-04-26_la_te_xi_t_1.jpg

Note – omega is the angular velocity in radians/second (just to be clear).

Measurement methods

You will not believe how many different ways I tried to rotate this iPod. I wanted to do it with stuff you could maybe find at home. My first failed attempt was to build a small Lego centrifuge (clearly, this guy knows how to build a home made centrifuge). I finally settled on this awesome PASCO rotating platform. It is great because you can stand or sit on it if you don’t mind getting sick from spinning. And then, how do you get it to rotate at a constant speed. I tried some complicated rotation device, but it turns out that if you just give it a good spin, it won’t slow down that much.

I found the iPhone app AccelGraph. Not a perfect app, but I think it is the best free one that could do the job. Originally, I had planned to use app AccelMeter because it has a great visual display. I was going to jailbreak my iPod so I could use VNC and record the screen. Failed. Anyway, using VNC makes it easier to start and stop the acceleration recording (especially since I mount the iPod with the glass down).

After making the video, I used Tracker Video Analysis to determine the angular velocity of the iPod. Note – autotracking feature on Tracker is the awesome.

Data

How fast was the first set up spinning? Here is a shot from the video. A couple of notes. I put the laser on the platform so that I could use that to measure the rotation rate if I needed to (turns out, I didn’t need it). The CD was taped there for reference of size, again – I didn’t need this. In this configuration, AccelGraph says the acceleration is in the negative y direction. Oh, I put a marker on the back of the iPod so that I could have a reference point. In this case the marker is centered on the “dot” over the “i” in the label that says “iPod”.

i-0acc487f9d05f798708cb7863dbc97e6-2010-04-26_vid00905mp4.jpg

After getting x, y, and time data from Tracker Video, I wanted to plot position vs. time and get a function to fit so that I could get the angular frequency. For some reason, Tracker Video was not quite fitting a sinusoidal function correctly. I used LoggerPro instead.

i-ec06d25930f2ffcbc267d1f8b6ce7830-2010-04-26_untitled_214_1.jpg

Both the x- and y-motion have an angular frequency of around 9.85 rad/sec. I am pretty happy with that. What about the data from AccelGraph? Here it is:

i-2d8e3e7b52d0a7d6249ab354cffc44ad-2010-04-26_ipodaccelvideo_1xmbl.jpg

Notice there is some fluctuation in the data. Even in the z-direction. I guess this could be of “bumps” and stuff. Really, I want the x and the y accelerations (and the total magnitude in the x-y direction) Oops – I just realized that AccelGraph gives the acceleration in untis of “g’s”.

i-ec2a2194f4cf9d4511d54e747c9731f8-2010-04-27_la_te_xi_t_1_5.jpg

The location of the reference point is at r = 0.174 meters. From the acceleration above, the sensor should be at:

i-d240daa4cf363655692ac77907599a04-2010-04-26_la_te_xi_t_1_3.jpg

Ok – now I will repeat the above for the iPod turned 90 degrees. Using the same methods, I get an angular velocity of about 11.2 rad/sec. Here is the data from the video:

i-91d897eea2d6d0075b831265f6312240-2010-04-27_untitled_2.jpg

The data from AccelGraph gives:

i-faaefefe8b258b09d61c55ab1bb12aed-2010-04-27_la_te_xi_t_1_4.jpg

This gives an “r” of:

i-076e0a59fb82539b1a634ac09acf049d-2010-04-27_la_te_xi_t_1_6.jpg

The answer

So, I know the distance from the center of the rotation to the sensor for the two orientations. Using some uber-drawing skills, I draw a circle with the same radius as the sensor for the two orientations and then put the two pictures on top of each other. Notice the marking circle on the back of the iPod. This was used to line up the two images.

i-bfdcd74bee054c011eb1f2242e9758bd-2010-04-27_untitled_6.jpg

The yellow box is the location where the two radii intersect. This could be the location of the acceleration sensor. Oh, I know. There are some problems. The biggest problem I had was measuring from the center of the circle of rotation. I kind of guessed. Perhaps I should have put a better marker on the rotation device indicating the center. Oh well.

Also, this would have been a great opportunity to show the error in the measurements and the propagation of this error in the location of the sensor. I did do this – mainly because I don’t want this post to be too long. You can do that as a homework assignment.

Comments

  1. #1 Alan B
    April 27, 2010

    Why not use a record player?

  2. #2 Rhett Allain
    April 27, 2010

    @Alan,

    Good idea – but I do not have one of these devices.

  3. #3 Fran
    April 27, 2010

    I agree with Alan B – I got a whole bunch of record players for free by trash-picking and helping people move. When you are moving, you don’t feel like moving your useless record player. About 2002-2003 was prime for trash picking them in my area.
    If you ever need a video for analysis of rotational acceleration, I have a bunch, which I will eventually put on youtube. All with one of my trash-picked turntables in the starring role.
    On the other hand, I am also trying to convince my department to spend the $419 or so for the awesome Pasco rotating platform. We really need one of those!

  4. #4 Rhett Allain
    April 27, 2010

    @Fran,

    I hope your department doesn’t see your comment or they will not get your spinning platform and instead encourage you to do some more dumpster diving.

    But you are right, I probably should find a record player.

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