MEMS Gyroscopes vs Accelerometers - When to use each?

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Wetmelon
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I am designing a motion tracking device and just discovered that there exists solid-state gyroscopes. My question is simply "What is the benefit or application of the MEMS Gyroscope compared with a solid state accelerometer?"

As far as I can tell, the accelerometer and the gyroscope can be used in much the same way, though one gives values in terms of acceleration and the other gives values in terms of angular velocity?
 
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You can use either, but if you want to measure angular velocity, you need a range finder built into the motion tracker. If you are using something on a car, for example, a simple accelerometer should suffice.
 
So the gyroscopes don't measure velocity? What do they output? Rotation angle?