Table Top Physics - Rotation - door


Richard sent me the following example:

A text book is placed flatly on a door near the doors outer edge. And someone closes the door shut. Would the book rotate and translate when it is separated from the door again, but it has all of its motion as it had when the door was closing?  
Consider a related situation? 
The book is extremely thin but it has the same mass as before just lest inertia, and it is placed on the door in the manner as before, and it touches the door on its thin side. When the door closes, the book would only translate when it is detached. 
Now let us consider the first case again, but this time when the door closes the book is broken up into atoms. Each atom would translate linearly and there would be no rotational momentum. 
I cannot make head or tail of these cases, if indeed these cases could actually occur within the confine of conservation of momentum. The 3 cases have the same total linear momentum, but only in case 1, can I see an additional rotational momentum. 
These cases shows that I should not have used an average position of an effective mass that is in a rotating body. And that the velocity of such a mass gives no measure of the linear momentum that is present in a rotating body. I thinking on this one.

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Martin: If we are thinking about the conservation of angular momentum I think we first have to choose where to measure the angular momentum around. I think I would choose the hinge of the door. I don't think we can choose the centre of the book because, as the door is closing, this will be travelling in a circle which in linear terms means that it is accelerating and is therefore not an inertial frame of reference.

So since we have chosen the hinge to measure the angular momentum about the hinge the, after the door has slammed is the perpendicular distance times the mass of the book. This is the angular momentum that the book had when the door hit the endstop, so the book is not spinning about its own axis at this stage.

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