What does an accelerometer measure?

[greypilgrim]

Hi

I'm confused about what an accelerometer actually measures. I downloaded an app that reads out the data of the accelerometer in my phone in all three dimensions. If I lay it flat on a table, it says something around 9.81 in the z direction and something around zero in the x and y directions. If I drop it (and record the data), the acceleration is about zero in all three directions.

This somehow makes sense since one feels weightless when in free fall. But still, the phone is only accelerated in the second case, and shouldn't an accelerometer measure acceleration?

 

[PeterDonis]

I'm confused about what an accelerometer actually measures.

An accelerometer measures proper acceleration; that is, the acceleration actually felt by an object. This can be thought of as the weight the object feels, divided by its (assumed constant) mass.

This somehow makes sense since one feels weightless when in free fall.

Exactly. And, conversely, one does feel weight when standing at rest on the surface of the Earth (or lying on a table). That's why an accelerometer gives a nonzero reading in the latter case, but not the former.

he phone is only accelerated in the second case

This is a different kind of acceleration, called "coordinate acceleration", and your experiment is a nice illustration of why the term "proper acceleration" was invented: you can't always feel coordinate acceleration, so we need a separate term to describe the kind of acceleration you can always feel, and which an accelerometer measures.

In relativity, in fact, coordinate acceleration is considered to be a convention, something you can change just by choosing different coordinates, not a direct observable. For example, when you drop your phone, it has coordinate acceleration with respect to (non-inertial) coordinates in which you, standing on the floor, are at rest; but it does not have coordinate acceleration with respect to (inertial) coordinates in which the phone is at rest. But it has zero proper acceleration regardless of which coordinates you pick--you can't change the accelerometer reading just by choosing different coordinates.