Saturday , May 8 2021

How to easily identify the accelerometer in an iPhone

Everyone should probably I know I'm obsessed with both physics and smart phones. If I can use my phone for a physics experiment, I'm fine. This is exactly what I'm going to do right now: use some physics to find the position of the accelerometer in the iPhone 7.

Your smartphone has a lot of sensors. One of the most common is the accelerometer. It is basically a minuscule mass connected to springs (not actual springs). When the phone accelerates in a particular direction, some of these springs compress to accelerate even the small mass of the test. The accelerometer measures this spring compression and uses it to determine the acceleration of the phone. With that, he will know if he is pointing up or down. You can also estimate how far you move and use this together with the camera to find out where the real world objects are, using ARKit.

So, we know that there is a sensor in the phone, but where is it? I'm not going to disassemble my phone; Everyone knows I'll never come back together again afterwards. Instead, I will find the position by moving the phone in a circular path. Yes, moving around in circles is a kind of acceleration.

Of course you already knew that circular motion was a kind of acceleration. Yes, you knew it because you've been in the car (you've probably been in the car). It turns out that the human body can also feel accelerations, even if sometimes we confuse these accelerations with gravitational forces, but we can still hear them. If you are sitting in a seat and the vehicle accelerates, it accelerates and you can hear it. Now if that car is spinning in a circle, you can also hear it. That spinning car is accelerating, even if it travels at a constant speed.

If you really want to understand why circular motion is a type of acceleration, you have to start with the definition of acceleration.

Here Δ means "change in". Therefore acceleration is the change in velocity divided by the change in time, ie a speed. But here is the key point. Both acceleration and speed are vector quantities. This means that they depend on direction and size. Since speed is a vector, you can have an acceleration simply by changing the direction of the speed. Moving in a circle at a constant speed means that there is really an acceleration.

If we have an object moving in a circle, the acceleration is pointed towards the center of the circle and depends on two things: the angular velocity (ω) and the circular radius (r). If you increase one of these values, the magnitude of the acceleration will also increase according to the following:

So maybe you can see where it's going. If I move a phone in a circle, I can measure both the acceleration and the angular velocity. From this, I can calculate the radius of the circle, which will be the distance from the center of the circle to the accelerometer. This should not be too difficult. In fact, I already did this experiment but it was a slightly different setup.

Actually, you can do it alone. In reality, all you need is a device that rotates the phone in such a way that it moves in a circle with a constant radius. For me, I used this beautiful rotating platform.

Note the addition of the ruler so that you can accurately measure the distance from the center of the circle to the bottom of the phone. I also put a small clamp at the end to prevent the phone from unloading from the platform. It would be bad.

The other thing you need is a way to measure both angular velocity and acceleration. Most phones have a gyroscope type to measure rotations so you can get both measurements with the phone. Although there are several apps to record sensor data on your phone, but I really like PhyPhox (both for Android and for iOS).

Now we are all ready. Start recording data and rotating the phone. As the angular velocity changes, the acceleration also increases (since the radius is fixed). Since the acceleration is proportional to the square of the angular velocity, I can track the acceleration against ω22. It should look like this (hopefully).

It seems to be linear, so it's okay. The slope of this line is 0.14138 meters with an intercept of 0.093 (rad / s)2 (which is close to zero). That track is the important part. It is the distance from the center of the circle to the sensor. I recorded the distance of the bottom of the phone at the center with a radius of 0.09 meters. This means that the accelerometer is 5.1 centimeters above the bottom of the phone.

But wait! And the side-to-side position? I can repeat the experiment with the side of the phone facing the center of the circle. Here are the data for that race.

In this case, I had the screen facing down with the side of the "sleep" button of the phone facing the center of the circle in a radius of 15.9 cm. The slope of the above line is 17.7 cm. This means that the sensor is 1.8 cm from the side. OK, this is technically wrong, but I will use it anyway. The 17.7 cm is actually the radial distance from the sensor. This will only give me the distance from the side of the phone if the sensor was halfway from the top of the phone. Oh well, this will be close enough.

So here is a diagram of my iPhone (looking from behind).

Sure enough that is where the sensor is located. Now I just need to disassemble my phone to check this result. Oh wait. I'm not going to do it.

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