# Accelerometer measures non inertial or inertial ref. frame

1. Dec 3, 2007

### ylim

Hi there,

I am doing some measurement using an accelerometer. I am rather confused with regards to whether I should be see an accelerometer as a non-inertial or an inertial sensor.

I have with me 2 commercial accelerometers evaluation board (analog to computer interface). One by the analog/crossbow collaboration board tells the static g as a +1g value, which is seen as a non-inertial reference frame whereas the other one by ST microelectronics with some third party tell static g as -1 (the inertial ref. frame).

Both of them tells positive acceleration swing from a positive axis acceleration and vice versa (this is okay).

Say now if I am interested to tell if I should be considering the centrifugal acceleration (I am mounting the accelerometer to a pendulem). Should I be taking the centrifugal acceleration as a non inertial or an inertial one? I am assuming that based on the fact that (Both of them tells positive acceleration swing from a positive axis acceleration and vice versa (this is okay).), I will be seeing a negative centrifugal acceleration (given positive direction to skyward). So I will not be able to see a non inertial centrifugal centrifugal accleration?

Hope to hear from you guys.

2. Dec 3, 2007

### D H

Staff Emeritus
Accelerometers are inertial-frame sensors. The reason an accelerometer registers 1g upward when it is not moving relative to the Earth can be explained from a classical physics perspective or from a general relativity perspective.

First, a little factoid. No device can be made that directly measures the force due to gravity. A wonderful sci-fi device called a "gravity shield" would be needed to perform such a measurement. An accelerometer is not a sci-fi device. It cannot measure the acceleration due to gravity.

From a classical physics perspective, an accelerometer is a device that measures the acceleration due to all forces acting on the accelerometer case except gravity. Suppose we have an accelerometer mounted on the surface of non-rotating planet with a gravitational force equal to that of the Earth. The downward gravitational force on the accelerometer case is balanced by an upward normal force exerted by the surface of the planet. (Note well: this is not a third law action-reaction pair. It is something different.) The accelerometer cannot sense the downward acceleration due to gravity, but it can sense the upward acceleration due to the normal force. Net result: the accelerometer registers 1g upward.

In general relativity, gravitation is a fictitious force rather than a "real" force. The GR point of view is that an accelerometer is a device that measures the acceleration due to all real forces acting on the accelerometer case, period. An accelerometer mounted on a the surface of non-rotating planet is not in an inertial frame! From the GR perspective, an accelerometer measures acceleration relative to an inertial frame, which in the case of the accelerometer on the surface of a planet is accelerating toward the center of the planet. The accelerometer is accelerating up relative to this frame. Net result: the accelerometer registers 1g upward.

3. Dec 3, 2007

### ylim

Hi DH,

I was hoping that you can answer my doubt though.

>>Say now if I am interested to tell if I should be considering the centrifugal acceleration (I am mounting the accelerometer to a pendulem). Should I be taking the centrifugal acceleration as a non inertial or an inertial one? I am assuming that based on the fact that (Both of them tells positive acceleration swing from a positive axis acceleration and vice versa (this is okay).), I will be seeing a negative centrifugal acceleration (given positive direction to skyward). So I will not be able to see a non inertial centrifugal centrifugal accleration?

Regards,

4. Dec 4, 2007

### D H

Staff Emeritus
If you mount an accelerometer to a pendulum, what real (non-fictitious) forces other than gravity act on the accelerometer?

One thing to keep in mind when mounting an accelerometer to a pendulum is that the accelerometer's case frame is rotating.

5. Dec 4, 2007

### ylim

1. translational acceleration
and
2. rotation?

Centrifugal can be seen as either a non inertial or an inertial ref. frame, that will account for differing signs. That is my concern.

6. Mar 7, 2010

### danany

Hi DH,
I have this question concerning accelerometers. I believe accelerometers measure "non gravitational" acceleration but I am unclear about the principles behind the belief by some authors that accelerometers are "self orienting". I am particularly interested in this because latest seismic surveys being carried out use 3 component accelerometers to measure P and S waves and no matter the orientation of the accelerometer it can be corrected based on "apparent gravity". I know accelerometers don't measure gravity, it measures the force acting on it wrt to a gravitational field but can't understand how these accelerometers can measure the force acting on it from the earth(as a result of seismic energy being generated by a seismic source) and at the time retain its orientation for onward correction.