Question

What is the length of material in yards delivered by a roll with a speed of 290 rpm and a diameter of 46 mm? (Note: assume the roll turns for 90 seconds.)

Answer 1

The length of material is 68.7 yards.

Explanation:

If the material is delivered in a roll, we can calculate how many material is delivered by turn (one rotation). In one turn it delivers (π*D) of material, its perimeter.

If the diameter is 46 mm, in one turn the material delivered is

`m=(\pi*D)=3.14*46mm=144.44 mm/rev`

As we know the rotational speed, we can calculate the amount of material delivered by unit of time:

`m=144.44 (mm)/(rev)*290(rev)/(min)=  41,887.6(mm)/(min)`

If the roll turns for 90 seconds (or 1.5 min) we can calculate

`m=41,887.6(mm)/(min)*1.5min=62,831.4mm`

As we need the result in yards, we can convert (1 yard=914.4 mm)

`m=62,831.4mm*(1yard)/(914.4mm) =68.7 \,yards`