Final answer:
To calculate the linear speed of a wheel with a diameter of 25 inches rotating at 11°/s, first convert the angular speed to radians per second, then calculate the linear speed using the formula v = rw. After converting the radius to feet, the linear speed equals approximately 0.136 mph.
Step-by-step explanation:
To find the linear speed of a wheel based on its rotational speed, we use the relationship between linear speed (v), the radius of the wheel (r), and the rotational (angular) speed (ω). The formula for linear speed is:
v = rω
First, we need to convert the diameter into radius by dividing by 2. The radius (r) of a wheel with a diameter of 25 inches is 12.5 inches. Since the angular speed is given in degrees per second (11°/s), we need to convert this to radians per second. We know that 360 degrees equal 2π radians. Therefore:
ω = 11°/s × (2π radians/360°) = 11°/s × (π/180°) ≈ 0.192 radians/s
Next, we convert the radius from inches to feet because the linear speed is usually expressed in feet per second or miles per hour. There are 12 inches in a foot, so:
r = 12.5 inches ÷ 12 inches/foot = 1.04167 feet
Now we can calculate the linear speed:
v = rω = (1.04167 feet) × (0.192 radians/s) ≈ 0.200 feet/s
To get a more familiar unit of speed, we can further convert feet per second to miles per hour (mph). There are 5280 feet in a mile and 3600 seconds in an hour, so:
v (mph) = v (feet/s) × (3600 s/hour) / (5280 feet/mile)
v (mph) ≈ 0.200 × 3600 / 5280 ≈ 0.136 mph
This is the linear speed of the wheel rounded to three decimal places.