So I think I've decided on a weapon for my robot, but now I'm unsure of how to go about the last bit of physics. I've modeled a spinning flywheel which is to be made out of a 4" iron caster which is clad in urethane. The flywheel is spun up, and a 16" steel rod, 5/8" in diameter, is thrown between the wheel and an idler. Rotational kinetic energy is converted to translational kinetic energy. But ignoring losses due to slipping, what is the final kinetic energy of the rod after a distance s, just before the rod meets a stopper and the whole wheel/rod system comes to a stop?
At first, I thought all of the kinetic energy would naturally be converted. But now I'm not so sure of myself. After all, the rod has to be accelerated over the distance s. As the wheel slows down, the rod picks up speed. It should be possible to calculate the final velocity of the rod just prior to position s, and thereby the final angular velocity of the wheel at the same time.
But on the other hand, since the system will inevitably come to a full stop, can we not say that all of the energy of the flywheel (barring frictional losses) is delivered to the spike? By this reasoning, the last bit of rotational energy is converted at the point where the rod stops, whether that be at point s or at the point where the rod mercilessly perforates the enemy. Does this sound like good reasoning?
For S&Gs, I'll go ahead and include my figures:
Flywheel at max angular velocity:
- $M = 1.13$kg
- $r = 0.0508$m
- $I = 0.000815$ (approximated as a simple disk)
- $ω = 556.1$ rads/s (maximum)
- $E_k = 126.02$J (rotational kinetic energy)
Rod, starting from zero initial velocity:
- M = .632kg
- s = 0.3048m (12" of travel distance)