In article ,
Jim Logajan wrote:

Alan Baker wrote:
Alan Baker wrote:
Jim Logajan wrote:
Alan Baker wrote:
Jim Logajan wrote:
Running the thrust line through M does _not_ guarantee you wont
get any couple.

It guarantees you won't get a couple from the thrust.

I think I see one of your problems. How many forces are needed for
a couple? Can one of those forces pass through the center of mass?

One. There only has to be a one force on a body in order for it to
experience to angular acceleration. That force just has to act on a
line that is not through the centre of mass.

I apologize, I was using the term "couple" incorrectly.

Not surprising, given that most freshman level college physics textbooks
don't even mention the concept (a pity). Most introductory mechanics
(statics and dynamics) textbooks, on the other hand, introduce the couple
concept in the first or second chapters.

But that doesn't matter to my argument.

It does matter in the sense that it is an important (perhaps essential)
concept needed to properly set up and solve these sorts of problems.
Another concept needed is the fictitious inertia force (m*A) that is
anchored at the center of mass and always points opposite the net
external force. That means there is always at least a second force around
to create a couple.

No. It is a *useful* concept, but it is in no way essential. Any problem
you can solve by taking couples and pure moments, you can solve without
reference to couples.

And the fictitious force you suggest would, if used, make the concept
conflict with its own definition. The very point of a couple is that it
can be represented by a pure vector moment, which by definition, cannot
accelerate a body linearly.

So if you say there is a couple when you talk about a system with a
single external force that isn't aligned with the centre of mass of the
body it is acting on, then your solution would suggest that the mass
doesn't undergo linear acceleration.


So ignore the first bit and answer my questions below:


Questions for you:

Do you believe that in the absence of any other forces, if the
aerodynamic forces act on a line that is not through the centre of
mass, will the aircraft experience angular acceleration?

It will undergo both angular and translational acceleration. The motion
of the system over time is generally not obvious and holds a few
surprises. For example:

A yes or no would have sufficed.


There is a related problem that often goes by the label "center of
percussion" (try Googling it) that shows that at the instantaneous point
in time that the system is placed at rest with respect a reference frame,
the instantaneous center of rotation in that reference frame is not at
the center of mass.

If you add thrust acting through the centre of mass to the situation,
will it change the angular acceleration?

When moving in a vacuum? No. When moving in a fluid? Yes it could. It is
not hard to imagine scenarios where that can happen.

No, it couldn't. The other effects that result in the thrust *might*
cause a change in the angular acceleration (increased/changed airflow
over the aerodynamic surfaces), that that isn't the thrust doing it.

--
Alan Baker
Vancouver, British Columbia
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