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The iPhone 4 Gyroscope teardown by iFixit:
The iPhone 4 contains a gyroscope -
run by what seems to be an off-the-shelf chip.
The iFixit crew and Chipworks used a scanning electron microscope to take a really close look at this amazing piece of nanotechnology
A mechanical gyroscope uses a spinning rotor in the centre to maintain a reference point in 3D space: if the frame is tilted, the angular momentum of the rotor resists movement, and the gimbals allow it to tilt.
The rotor can be driven using induction, so it is contactless. The version shown has three "degrees of freedom" - it can move around any axis.
But how do you make it small enough to fit inside a mobile phone?
Answer: a microelectro
mechanical system (MEMS), an embedded system that integrates electronic and mechanical components at a microscopic scale. iFixit says that the AGD1 2022 FP6AQ chip (marked red) found in the iPhone 4 is a MEMS gyroscope, rumored to be designed by STMicroelectronics. 
Chipworks says that the iPhone 4's gyroscope is almost identical to another off-the-shelf one, from STMicroelectronics. Here's that one: it consists of this thin plate of etched silicon, called the "proof mass", which oscillates when you apply a voltage across a capacitative gap. (The gap is below the chip die you see here.)
The masses are the quadrants on left and right of the picture. Tilt the chip, and the masses move - generating a voltage change at the capacitative gap, and on "finger capacitors" (the fronds from the middle of the bottom and top).
Careful interpretation by another chip of the electrical signal generated tells you how much and in which axes the gyro chip has been moved.
For a more detailed explanation, see Conventor's
Once you've got your signals, you need to convert them into information. The V654A ASIC (application-specific integrated circuit) die converts the tiny capacitive signals from the MEMS die into a digital signal, which is fed into the iPhone 4's processor.
by: www.iphone4g4.com
The gyroscope can distinguish movement with an accuracy of up to 2,000 degrees per second - over 600 times more detailed than the movement of the second hand on a clock. Now we're down to nanotechnology. Chipworks used a scanning electron microscope (SEM) to view the LYPR540AH tri-axis MEMS gyroscope. Though not part of the iPhone 4, it shows the detail. The proof masses are on the right and left of the die. More nanotechnology: MEMS gyroscopes can feature amazing oscillator designs, such as this Kionix gyroscope.
You'd never see it because it's under a dust cover - but that's good, because on this scale a single human hair (100 micron thick) would ruin its functionality. A MEMS oscillator with the outer casing removed: an ASIC, with its custom gate array, sits on top of the oscillator, which is bonded to it by the obvious wires. The two are then encased in plastic to make the chip.
Scanning electron microscope view of the oscillator used in the SiTime SI8002AC. At this scale, a human hair is as wide as the central item. That's nanotechnology in everyday life - achieved through the advances in microengineering.
Alternatively, you could just carry a full-sized gyroscope in your pocket. But after seeing these pictures, would you want to?