Why does a gyroscope precess when tilted?

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[SOLVED] Gyroscope problem

Homework Statement



http://www.badongo.com/pic/3634214

The Attempt at a Solution



I think this topic is very difficult to grasp, but I've understood that when a torque is applied on the wheel, its angular momentum will chase that torque. One will therefore expect the small wheel to tilt against the woman. I know that the big wheel will start to spin, but why?
 
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That was very helpful and easy to understand. Physics is all too often made more complex and difficult than it is.