epepep said:
This is from my retired physicist friend. He's fantastically intelligent -- nearly half as smart as he thinks he is -- which is a bunch. But he's still wrong sometimes, just like everybody else...
2. On first thinking, "no recoil" seems reasonable.
Actually, it isn't at all reasonable. I'm surprised that someone who is a retired physicist could make this mistake. I was actually surprised that there is so much confusion about this very simple issue even by non-physicisits. Especially after the correct answer was pointed out a number of times.
If you shoot bullets out of a gun, they carry momentum. This causes recoil, because momentum is conserved. That's really all there is too it!
Working out the details in terms of the motion of the body is slightly tricker, but not a lot so, and has already been done by myself in this thread a couple of times.
I think I've already suggested thinking about a rotating rod on a frictionless surface a couple of times already. Imagine the rod initially has a zero average velocity, i.e. it's not moving except the fact that it's spinning. If a small piece of this rod breaks off, the small piece goes forwards, and the large piece goes backwards!
There are a number of ways of seeing this, of which the fact that the center of mass of any closed system stays at the origin is only the simplest.
A more complex way of seeing this may be simpler for some people (?). If one actually draws out the velocity of each piece of the rod as a function of position, one finds that it's a linear function of position, i.e.
v = -5*w at x=-5, v=0 at x=0, v=5*w at x=5
which can be summarized by the simple equation
v = w*x
So what happens if the piece from x=4 to x=5 breaks off? It obviously moves forwards. What happens to the remeaning parts of the rod?
Well, each small piece of the rod maintains its velocity. We can decompose the velocity of the large rod segment which strteches from (x=-5 to x=+4) as the sum of a rotation around it's new center of mass (at x=-.5) and a linear velocity as follows:
v(x) = w*x = (x+.5)*w - .5*w
The first term, (x+.5)*w, represents the velocity due to the rotation around the new center of mass at x=-.5, note that this term is zero at x=-.5 as desired, because x+.5 represents the distance between 'x' and the center of mass which is at -.5. x - (-.5) = x+.5.
You can think of this as
v(x') = w*x' - .5*w, where x' is the distance of a point from the new center of mass, so that x' = x+.5.
The second term, -.5*w, represents a constant linear velocity that the rod segement as a whole has (a negative velocity).
This result, which could have been and was predicted from the conservation of momentum, should not be a surprise, especially after it's been explained so many times.
The small segment of the rod shoots forward, and the large segement recoils backwards. The center of mass of the enitre system stays at the origin. The total linear momentum of the small piece in the forwards direction is equal but opposite to the total linear momentum of the larger piece, because the total momentum of the system is zero.