To determine the rotational frequency needed for a baseball pitching machine to throw an 80 mph fastball, you would need to know the circumference of the wheels (since the speed of the pitch is determined by the speed of the wheels), as well as the pitch's speed in relation to the speed of the wheels.
The circumference of the wheel can be found by using the formula C = 2 * pi * r where r is the radius of the wheel. The radius is half of the diameter, so for a 30 cm diameter wheel, the radius is 15 cm. Therefore, the circumference of the wheel is:
C = 2 * pi * 15 cm = 94.25 cm
To convert the speed of the pitch (80 mph) to cm/s we can use the formula:
Speed(cm/s) = Speed(mph) * 1.46667 * 6076
Speed(cm/s) = 80 mph * 1.46667 * 6076 = 472480 cm/s
Finally, we can use the formula:
frequency(RPM) = (Speed of the pitch(cm/s))/( circumference of the wheel(cm))
frequency(RPM) = 472480 cm/s / 94.25 cm = 5011.87 RPM
So the wheels need to rotate at about 5011.87 revolutions per minute to pitch a 80 mph fastball.