Re: [HOE] Ummmmmmm... WOW! (minor spoilerish stuff, maybe)

[Matt Crawford <matt@severian.chi.il.us>]

> Oh! and before I forget, the chances are that firing the weapon
> while unbraced would start a character tumbling, rather than
> rocketing through space, since it will (almost certainly) not be
> held and fired along the axis of the person's center of
> gravity. Just something else to think about. . . .

OK, I'll take this one on as penance for posting so manay consecutive
messages.  This time I don't know the answer (fast or slow spin) in
advance.  But there will be some estimating ...

I'm going to suppose a person's center of gravity is a bit above the
navel and that a Chinese SGS assault rifle is fired from the shoulder.
The mass of the bullet is 3.5x10^-3 kg and the velocity is 10^3 m/s.
The impulse on the shooter is about 0.5 m from the center of mass,
for a total imparted angular momentum of 1.75 kg m^2/s.

Now for the tough part - the moment of inertia of a human about a
diagonal axis.  About a vertical axis it would be roughly
I1 = M W^2/2, where W is the width of the torso.  The moment of inertia
around a "horizontal" axis would be somewhat less than I2 = M H^2/12,
where H is the height.  (For comparison, the moment of inertia of a
sphere about any axis is (2/5) M R^2.)  For an axis perpendicular to
the navel-shoulder line I'm going to handwavingly take the average,
and let H = 2m and W = 0.5m, M = 100kg.  I come up with 21 kg m^2.
Dive the angular momentum above by this and get the angular velocity
of 0.083 radians/second, or 0.013 revolutions per second.  About
3/4 rpm.  Darned annoying I'm sure, but not cinematically spectacular.

Of course, a more powerful gun ...