Before we get into the nitty gritty of things, let's understand what a gyroscope actually does.
According to Wikipedia's definition, "A gyroscope is a device for measuring or maintaining orientation, based on the principles of conservation of angular momentum." The key phrase is measuring or maintaining orientation, which is the exact reason an iPhone 4 contains one of these gizmos.
A mechanical gyroscope - like the one shown on the left - uses a spinning rotor in the center to detect changes in orientation.
The iPhone 4 utilizes a microscopic, electronic version of a vibrational gyroscope, called a MEMS gyroscope.
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