Someone asked for an explanation or definition of "inertial force". Unless
I missed it, no one responded; so here is a crack at it. I don't really
want to get onto the psuedo-force thread at the moment; preferring to
resolve the weighty thread, which I think we are very close to doing with
John&John's summaries.
Inertial Forces: (Newtonian viewpoint)
One may use any frame of reference one desires in measuring the position,
velocity and acceleration of an object. Without a priori knowledge as to
whether or not the frame of reference is inertial or not, one may attempt
(successfully) to analyze the situation by saying:
sum of forces = mass * acceleration
One notices an odd fact. For some frames of reference you will have some
terms "forces" on the left-hand side that are proportional to the inertial
mass of the object in question. These are the inertial forces.
Example: penney on the rotating LP album. Choose a frame of reference
painted on the LP (co-rotating frame). One of the force terms will be given
by m*r*omega^2, where omega is the rotational speed of the LP and r is the
distance the penney is from the center of the LP. This force is directed
outwards. And is an inertial force. (it even has a name which is a dirty
word in some circles, so I omit it here)
Inertial forces have some odd properties compared to other forces.
1) They are always proportional to the inertial mass upon which they are
acting. (which I gather is why they are known as inertial forces.)
2) There exist reference frames for which they are zero in magnitude. These
frames are the familiar inertial reference frames. (in short, they are
frame dependent).
3) Newtonian viewpoint says, gravity is not one of these types of forces
since the gravitational is proportional to the gravitational mass of the
object.
4) Einstein viewpoint. The equivalence principle should be taken literally
to mean that gravitational mass and inertial mass are equivalent; therefore
the gravitational force can be viewed as being equivalently an inertial
force. But this is another story . . .