Velocity, Radius and Angular Speed - Finding Units I have been trying to figure this one out for two days, and I really have no idea what to do. 
To begin with, I need to know what units will be produced in the following situations:


*

*Velocity's units when angular speed and radius are rpm and feet, respectively. (I think it is feet/minute)

*Anuglar speed's units when radius and velocity are foot and feet per minute, respectively. (It stays as feet/minute?)

*Radius' units when velocity and angular speed are mph and rpm, respectively. (I am guessing it will come out as miles, according to what my teacher tried to communicate)


Those are just a few issues, but there are more. I believe that, if I am correct/find why I am incorrect, I will be able to apply the concept to the other problems.
The second problem I am having is that I have a problem where:
Velocity is 50 feet/second, Angular Speed is 100 revolutions/second and I need to find the radius in miles. 
According to what I know, velocity is angular speed times theta, so I just have to divide by angular speed. However, I do not know where to go when there are different units.
I know it is a lot of text, but I appreciate anyone who can help me; my teacher said she is preoccupied and cannot answer any more of my questions today, so I'm stuck.

Angular speed has to be some measure of angle divided by some measure of time.  In your second bullet point it will probably be revolutions per minute (rpm).
You presumably have some formula saying velocity is related the product of radius and angular speed.  Here you probably have $$50 \text{ feet/ second} = r  \times 2\pi \text{ radians/revolution }\times 100  \text{ revolutions/ second}$$ which gives a radius of $r = 0.25 / \pi \text{ feet}$, not very much.  If you must convert it into miles, then use $1 \text{ mile} = 5280 \text{ feet}$, though that will give you an even smaller number.     
