Could you create a "fast forward" machine using something like an accelerating Ringworld? If you had a large cylinder in space with people on the inside surface and you started it spinning at a constant acceleration of 1G until it was spinning at near light speed (so the tangential velocity of any point on the cylinder's surface was near light speed) would the people on the inside be in a safe 1G environment where their time would be running much slower than people outside the cylinder (so let's say you leave it spinning for a week but the people inside only experience an hour or so, hence a "fast forward" machine)?
Basically my confusion lies with whether the gravity the people on the inside of the cylinder experience is a consequence of the velocity of the spinning or the acceleration of the spinning. Would this be a "fast forward" machine or a "people squishing" machine?
 A: 
Basically my confusion lies with whether the gravity the people on the
  inside of the cylinder experience is a consequence of the velocity of
  the spinning or the acceleration of the spinning.

The gravity the people on the inside of the cylinder experience is a consequence of the speed of the spinning. That's because the direction they are moving is continually changing. Any change of velocity is acceleration, even if the speed doesn't change.
With a little bit of calculus, it can be shown that for a body to travel in a circle of radius $r$, with constant speed $v$, requires a constant centripetal acceleration $a_c$ given by 
$$a_c = \frac{v^2}{r}$$
If you want to know the derivation of that formula, please see the section on acceleration in the Wikipedia article on circular motion.
If you continually increase the rotation speed of your cylinder, the force on the cylinder, and the people inside it, will keep increasing. The people will get crushed, and the cylinder will get torn to pieces, long before the rotation speed gets anywhere near $c$, the speed of light.
So your "fast forward" machine is impossible, I'm afraid.

I've had second thoughts about this. We don't need a high acceleration to get near lightspeed. As Ján Lalinský mentions in a comment, we can make the acceleration small by making $r$ large. Rearranging the acceleration formula, and using $c$ for the speed, and standard Earth gravity $9.80665 m/s^2$ for the acceleration, we get $r = 9.16475 \times 10^{15}$ metres, which is 353.823 light-days.
Of course, we can't actually reach lightspeed, and the amount of energy required to accelerate a physical ring that size to a high enough speed to get significant time dilation is extremely large.
Also, once we get to those speeds, the ring will experience significant length contraction. That is, the circumference will be equal to $2\pi r \gamma$, where $\gamma$ is the Lorentz factor, which is the same factor affecting time diation. Eg, for a ring spinning fast enough so that 1 hour of ring time is 10 hours Earth time, then the circumference of the ring is $20\pi r$.
So there isn't much point constructing the ring, we might as well just build a normal spaceship.
