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i was reading a book in which it is written that if a rigid body have both rotational(with angular velocity 'w' about its center of mass)and translation(with velocity 'v' of center of mass) motion then the whole motion can be treated as an equivalent motion of pure rotation about instantaneous center of rotation with same angular velocity 'w'.my doubt is that how can angular velocity be same as we are changing our reference point and angular velocity is a function of reference point?please explain this and if possible give me the mathematical proof of this.i am trying to prove it since last two days but failed every time.

Thanks

Arvind