Complete in Metric Conversions:

What is the tip speed (ft/min) of a 21 inch long rotary lawn mower blade that is connected to the output shaft of an engine operating at 3400 rpm?

To find the tip speed in ft/min of the rotary lawn mower blade, we'll need to use the following steps:

Step 1: Convert inches to feet.
Since the length of the blade is given in inches, we need to convert it to feet. There are 12 inches in a foot, so the length of the blade in feet can be calculated by dividing the length in inches by 12.

21 inches ÷ 12 = 1.75 feet

Step 2: Calculate the circumference of the blade.
The circumference of a circle can be found using the formula: circumference = 2πr, where r is the radius. Since the blade is a circular shape, we need to find the radius of the blade first.

The radius can be calculated by dividing the length of the blade by 2π (approximately 3.14159). Let's calculate it:

1.75 feet ÷ (2 × 3.14159) = 0.2783 feet (rounded to 4 decimal places)

Step 3: Calculate the tip speed.
The tip speed of the blade can be found by multiplying the circumference of the blade by the rotational speed of the engine. However, we need to ensure that the units are consistent. Since the rotational speed of the engine is given in revolutions per minute (rpm) and we want to find the tip speed in ft/min, we need to convert the rpm to revolutions per foot.

To convert rpm to revolutions per foot, multiply the rpm by the circumference (in feet) of the blade:

3400 rpm × (2π × 0.2783 feet) = 6069.2 ft/min (rounded to 1 decimal place)

Therefore, the tip speed of the rotary lawn mower blade is approximately 6069.2 ft/min.