Here is a mind boggling case involving rotational momentum and translational
What if you had a situation like this?
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.
Yes, these are interesting examples, I tend to think in pictures so I
will try to draw some diagrams and put them on the website when I get
time. When I get this type of problem I use the following principles:
1) The angular momentum of a solid object depends on the point that we
are measuring to rotation around.
2) Even a non-rotating object, which is travelling in a straight line
in the inertial frame has a non zero angular momentum if its trajectory
does not pass through the point we are measuring to rotation around.
3) Angular momentum is only conserved when we are measuring the momentum
about the same unchanging point for all objects.
4) Angular momentum is only conserved for closed systems, we have to be
careful to take into account all external influences on the system.
What do you think of these 4 laws? 1 more than Newton!
I also thought of another example. And this would involve 1) and 4)
A small boat is on water and has three passengers of equal mass. One passenger
is in the center of the boat and the other two are at the ends.
Before this occured, the last passenger ran and jumped unto the still
boat into his seated position. The boat will move away differently if
the last person was the middle passenger or the end passenger. However,
the momentum of the last person jumping on the boat may be contant. Thus
the position is what causes the variation (1) and the closed system would
contain the 3 passengers and the boat (4)
Where I can, I have put links to Amazon for books that are relevant to
the subject, click on the appropriate country flag to get more details
of the book or to buy it from them.
Game Physics - This book has some useful stuff, its more of a textbook, not
a step by step guide (although it does have a disc with a lot of C++ code).
About the first third of the book is a physics textbook with theoretical exercises,
the middle bit covers physics engine topics, and the last third of the book
covers mathematical topics. I think I would use this book as a reference book
to lookup the theory behind something I might be working on rather than a book
to work through in order.
Commercial Software Shop
Where I can, I have put links to Amazon for commercial software, not
directly related to the software project, but related to the subject being
discussed, click on the appropriate country flag to get more details of
the software or to buy it from them.
Dark Basic Professional Edition - It is better to get this professional
This is a version of basic designed for building games, for example to
rotate a cube you might do the following:
make object cube 1,100
for x=1 to 360
rotate object 1,x,x,0
Game Programming with Darkbasic - book for above software