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I have an accelerometer which measures 1g along the z axis when resting on a table. I don't understand why this is because the net force on the accelerometer is zero along the z-axis as the force of gravity is cancelled by the normal force exerted by the table on the accelerometer. And as the net force on it is zero the acceleration should be zero too right? What am I missing here? In which frame of reference am I getting the accelerometer readings?

Qmechanic
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Soham
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  • How about gravity? Last time I checked that was 1g. – hdhondt Aug 13 '19 at 05:32
  • The fact that 1g (or pretty close depending on just where you are) is readily available makes a simple test for the functioning of accelerometers that measure in the few to perhaps 100s of gees (depending on how sensitive they are). – Jon Custer Aug 13 '19 at 13:20

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The accelerometer in your phone is measuring the upwards force exerted on the phone by the surface of the table. You can convince yourself of this very easily by dropping your phone (onto a soft surface!) and measuring the accelerometer readings while the phone is falling using a suitable logging app $^1$. You'll find the accelerometer shows zero while the phone is falling freely and returns to showing $1g$ when the phone has come to rest.

Understanding exactly what is going on is surprisingly subtle and in fact is the basis for Einstein's theory of general relativity. The basic idea is that gravity is not a force, so while the phone is falling freely there is no force acing on it. That's why the accelerator shows zero while it's falling freely. There is only a force acting on the phone when something else is pushing on it, like the surface of the table, your hand when you're holding the phone or indeed anything else that is stopping the phone from falling freely.

If you're interested to learn more about this I go into more detail in my answer to If gravity isn't a force, then how are forces balanced in the real world?

$^1$ Just for fun I did this experiment using the Physics Toolbox app to record the accelerometer readings when I dropped my phone ono my bed, and I got this graph:

Phone accelerometer

For more on this see the discussion in the chat room starting here.

John Rennie
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  • Independent on the inner mechanism, wouldn't the fact that the phone moves on an circular path useful to justify the reading in a classical way? – Alchimista Aug 13 '19 at 09:31
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If it were in freefall in a vacuum it would read zero. It is pressed against the table with 1 g of gravity, so it is the same as if it were outside of any gravity field and the table were accelerating it at 1 g.

Adrian Howard
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iPhones use the Apple motion coprocessors to collect sensor data from integrated accelerometers, gyroscopes and compasses and offload the collecting and processing of sensor data from the main central processing unit (CPU).

That data is processed by numerous apps in different ways as shown below with an iPhone at rest on a table.

enter image description here

Physics Toolbox Suite has a g-force readout which gives you the "apparent" value of the gravitation field strength (zero when the iPhone is in free fall) and a linear accelerator output which shows the acceleration of the iPhone.

Sensor kinetics pro gives a value for the "apparent" gravitational field strength with a value of zero if the iPhone is in free fall.

Acceleration sensor logger (Pro Acceler Log) also gives a value of the "apparent" gravitation field strength with a value of zero if the iPhone is in free fall.

So you have to interpret the data as you wish.

Farcher
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