Velocity / Speed loss by shifting to a larger radius

If there was a free-spinning effective weight of 20 lbs. at a 20" radius rotating at 180 rpm (15.7 fps?) and a force of 20 foot pounds was added, what would be the increase in velocity/speed? (Ignoring friction and wind losses).

 

I am an independent inventor. This is not homework. I already have a degree, it is just not in Engineering. The force I am adding is rotational force or torque. This is a device I am building and I am looking to optimize the design. Ideally I would like to know the "payoff" for the input of energy into the system. The source of the force is not important. It could be as basic as a push from a human being's hand.

 

Thanks for the reply... I guess I am not good at stating the problem, sorry for the lack of Engineering savvy....Assume for illustrative purposes that 20 pounds was added to the downstroke for a distance of one foot and was removed immediately after that one foot of distance. What I am, basically, looking for is the effect on one rotation. Specifically, I wish to find out what is the maximum gain in velocity from that one input of 20 foot lbs. for one revolution.

 

Thanks for that. I am sure you are right about SI units. My goal was just to see if I could get a hard number for mps or fps or rpm that resulted from the energy input to the vertical rotation. Assuming 180 rpm of original speed . (I added downstroke to imply vertical rotation). My degree is in Communications, (Graduated with Honors). I am much better with words than numbers, although Baluncore is correct that I made quite a few errors in my statement of the problem, including the OP Question. Currently, I am going through a health condition that reduces my cognitive skills. Originally, I attempted to become an Engineer but I quickly learned I am incapable of doing the math. This is one of the few places I can go with help on my inventions when I get stopped by the math. I, literally, would not have a clue as to do what you suggest, even though it is obviously the way to go. Let me know if you know of anywhere I can get something like this calculated, even if it is for a fee. Just need to keep it reasonable. Thanks.