I think I have found something that could spin the small wheel end of the Vex High reduction Gearbox.
Although, right now I can’t calculate the motion and speed etc, I am sure this engine would give it a run for its money with a
Maximum power: 108,920 hp at 102 rpm!!!
Maximum torque: 5,608,312 lb/ft at 102rpm!!!
The other end would probably result in liftoff at the speed it would be spinning!

244,140,625:1 is the ratio posted on the youtube video.
The engine outputs 67,299,744 in-lbs of torque.
Stall torque of a vex motor is 6.5in-lbs(just for reference ;D)
I don’t know enough of the physics to do the rest, but if the whole system was frictionless, it would work =). Otherwise, even that mighty engine might have to use a gearbox to spin it.

where 102 RPM is the speed at the point of maximum torque, 244,140,625 is the ratio and the rest is the diameter of the 5" wheel.

That gives: 9,935,593,563 metres per minute or 165,593,226 metres/second

~166,000 km/second in other words which is over half the speed of light and thus probably impossible. On the other hand, I’m sort of tempted to think that gearing that engine down to give more reasonable speeds of rotation would work far better