FRC Motor Selection for Disc Launcher

Selecting a motor for the disc thrower will need to account for:

The necessary output speed of the wheel launcher
The torque applied to the wheel.

The disc weighs 0.18kg (
Field = 50' max

Speed of Launcher:
Our team did several trials for how fast a disc must be thrown to not drop over 50feet (~15.4meters) to cross the game field. 
The trials results ranged from 1.2seconds to 1.5seconds. 

We use the 1.2seconds as the time to cover 15.4meters.
This provides a linear speed of 15.4m/1.2s = 12.82m/s

A wheel travels it's circumference(pi*diameter) every revolution (distance/rev).
This provides Pi*Diameter/Revolution

Our team examined 6", 8" and 12" wheels

Now determine how fast the launcher must spin to achieve a linear speed of >12.82m/s

diameter circumference
6" 18.84955592
8" 25.13274123
12" 37.69911184

Then convert inches to meters for units

Then use the linear speed of 12.82m/s to determine the rev/sec needed for each diameter wheel
=(linear speed)/(meters/rev)

Then, for compatibility with motor units convert the rev/sec to rev/minutes

If there is any gear ratio between the motor output and the launching wheel then that must also be included in the rpm to the motor.

The actual excel sheet is a little easier to see the diameter linked to the output:
diameter circumference meters/rev rev/sec rev/min
6 18.84955592 0.478974334 26.765526 1605.931563
8 25.13274123 0.638632445 20.0741445 1204.448672
12 37.69911184 0.957948667 13.382763 802.9657814

The spinning objects are measured several ways. 
Cycles per second = Hertz
Radians per second = 2*pi*Hertz
Revolutions per second = RPS = Hertz
Revolutions per minute = RPM = Hertz*60

Motors are usually rated in Revolutions per minute (RPM)
The units for linear speed is meters/second