Table Top Physics - Rotation - boat

By: Nobody/Anonymous - nobody
RE: 2D Rotation to Linear Momentum Conversion
2005-02-06 10:07

Here is a mind boggling case involving rotational momentum and translational momentum.


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.

Any comments on this Martin?

By: Martin Baker - martinbaker
RE: 2D Rotation to Linear Momentum Conversion
2005-02-07 01:54

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!

Martin

By: Richard - redeyes2003
RE: 2D Rotation to Linear Momentum Conversion
2005-02-07 13:02

I agree with these laws.

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)