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In the unit of accelerometer and linear acceleration, I see that accelerometer is angular and the linear acceleration is linear. There is the impact of gravity on the accelerometer. However, considering a wearable sensor, for example, a smart bracelet, suppose that we have a 3-axis accelerometer sensor in it. Suppose that we only move our wrist on $z$-axis (ex. move up) without moving on the $x$- and $z$-axis. linear acceleration on $z$-axis gives us our speed (m/s^2) but what accelerometer does. I have some difficulties imagining the value given by z-axis of the accelerometer. What means, visually, angular acceleration?

Example of a case: Suppose that I am walking and I hand my phone to my friend who is walking next to me. I am interested in how I hand the phone. I want to work on the pattern of this. For example: Let's say I'm looking for the answer to the question of whether each person has a unique phone handing pattern. Let the sensor be a sensor integrated into the smartphone.

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    $\begingroup$ It depends on what you are doing with the sensor. You refer to materials not provided so we cannot know what you are talking about. $\endgroup$
    – DKNguyen
    Commented Dec 15, 2021 at 15:14
  • $\begingroup$ @DKNguyen, Suppose that I am walking and I hand my phone to my friend who is walking next to me. I am interested in how I hand the phone. I want to work on the pattern of this. For example: Let's say I'm looking for the answer to the question of whether each person has a unique phone handing pattern. Let the sensor be a sensor integrated into the smartphone. $\endgroup$
    – Mas A
    Commented Dec 15, 2021 at 15:17
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    $\begingroup$ @MasA Your question starts with "In their formulation, I see that one is angular and the other one is linear." We have no idea who "their" refers to, or what "one" and "the other one" might be. Please clarify what you're talking about. We can't answer without understanding what you're asking. $\endgroup$
    – Mike
    Commented Dec 15, 2021 at 15:24
  • $\begingroup$ I tried to revise my question. I hope it is better now. $\endgroup$
    – Mas A
    Commented Dec 15, 2021 at 15:32
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    $\begingroup$ If you are analyzing a motion event that does not care about gravity, and gravity is always there and the same direction, what does it contribute to your analysis other than offset errors? That drift with time no less. $\endgroup$
    – DKNguyen
    Commented Dec 15, 2021 at 15:46

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You are not only ignoring gravity. You are also ignoring the force from the ground that holds you up. If only gravity acted on you, you would be in free fall. The force from the ground that prevents free fall is equal and opposite to gravity. So the total force you are ignoring is $0$.

One (not necessarily practical) way to make a z-axis accelerometer would be to put a bead on a vertical wire and attach the bead to a string. If the accelerometer accelerates in the vertical direction, the bead will get left behind. The wire will move upward, compressing the spring. The compressed spring will push upward on the bead until it moves along with the rest of the accelerometer. You measure acceleration by measuring the compression of the spring.

Sitting still, the weight of the bead compresses the spring. You mark that length as an acceleration of $0$.

In free fall, the spring would be longer. You mark that length as an acceleration of $1$ g downward.

You mark other lengths similarly.

There are better ways to make an accelerometer, but this should help you see how they are affected by gravity.

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