how to measure rate of rotation using using smartphone sensors

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I am trying to make a game in which the rate a game event occurs (such as climbing or rowing or spinning a wheel) is proportional to the rate at which the user rotates/spins an android device, using either world coordinates or device coordinates.I would like to use accelerometer and gyroscope(or any sensor present on current generation smartphones)

I have looked at calculating distances using accelerometer and Indoor Positioning System based on Gyroscope and Accelerometer . Apparently accurate position/velocity detection is impossible using only these two sensors due to noise.

So my question is : Is it still possible to measure the rate of spinning or rotating of a current gen smartphone.If so how and which types of rotation can be measured?

I do not care about exact displacement or velocity of the device , just some fairly accurate measurement of rate of some repetitive motion to drive game events.

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