A propeller blade has a period of rotation of 0.400s. What is the speed of the outer tip of the propeller blade if the tip is 1.20m from the hub?
To find the speed of the outer tip of the propeller blade, we can use the formula:
v = (2πr) / T
Where:
v = speed of the outer tip of the propeller blade
r = distance from the hub to the tip of the propeller blade
T = period of rotation of the propeller blade
Given that the period of rotation (T) is 0.400s and the distance from the hub to the tip of the propeller blade (r) is 1.20m, we can substitute these values into the formula:
v = (2π * 1.20) / 0.400
First, let's calculate 2π * 1.20:
2π * 1.20 = 2.40π
Now, let's divide 2.40π by 0.400:
v = (2.40π) / 0.400
To get the value of v, we can calculate the numerical value of π as approximately 3.14:
v = (2.40 * 3.14) / 0.400
v ≈ 18.84 / 0.400
v ≈ 47.1 m/s
Therefore, the speed of the outer tip of the propeller blade is approximately 47.1 m/s.