Assuming that a table saw blade has a diameter of 12 inches and spins at 3450 revolutions per minute (RPMs), use the unit conversion techniques you have learned from the material in 2-A to determine how fast the tip of the teeth of the saw blade are traveling in miles per hour.
To determine how fast the tip of the teeth of the saw blade is traveling in miles per hour, we need to follow these steps:
Step 1: Convert RPM to inches per minute
Since the saw blade spins at 3450 RPMs and we want to find the speed in inches per minute, we can use the following conversion:
1 revolution = circumference of the blade
Circumference of the blade = pi × diameter
Circumference of the blade = 3.14 × 12 inches
Now, we can calculate the speed in inches per minute:
Speed (inches/minute) = RPM × Circumference of the blade
Speed (inches/minute) = 3450 RPM × (3.14 × 12 inches)
Step 2: Convert inches per minute to miles per hour
To convert inches per minute to miles per hour, we need to perform two conversions:
1 mile = 5280 feet
1 foot = 12 inches
To find the speed in miles per hour, we will use these conversions:
Speed (miles/hour) = Speed (inches/minute) × (1 foot/12 inches) × (1 mile/5280 feet)
Now, let's perform the calculation:
Speed (miles/hour) = Speed (inches/minute) × (1 foot/12 inches) × (1 mile/5280 feet)
Speed (miles/hour) = (3450 RPM × 3.14 × 12 inches) × (1 foot/12 inches) × (1 mile/5280 feet)
Simplifying the equation, we get:
Speed (miles/hour) = 3450 RPM × 3.14 × (1 mile/5280 feet)
Calculating the final answer:
Speed (miles/hour) = 3450 RPM × 3.14 × (1 mile/5280 feet)
Speed (miles/hour) ≈ 61.73 miles/hour
So, the tip of the teeth of the saw blade is traveling at approximately 61.73 miles per hour.