Angular Speed and Velocity of a Helicopter Blade
a) What is the average speed of the blade tip in the helicopter's frame of reference, in meters per second?
a) To calculate the average speed of the blade tip in the helicopter's frame of reference, we need to convert the given value of revolutions per minute to radians per second. Given: Number of revolutions per minute (rpm) = 110, Radius of the blade tip (r) = 6.5 m. Explain the formula and methods to calculate the average speed in meters per second.
b) What is the average velocity over one revolution, in meters per second?
b) How do we calculate the average velocity over one revolution in the helicopter's frame of reference? Discuss the formula and process involved in determining the average velocity over one revolution.
Answer:
a) The average speed of the blade tip in the helicopter's frame of reference is approximately 75.08 meters per second. b) The average velocity over one revolution in the helicopter's frame of reference is approximately 75.94 meters per second.
Explanation:
a) Calculation of Average Speed:To calculate the average speed of the blade tip, start by converting the number of revolutions per minute to radians per second using the formula: angular speed (ω) = (2π × rpm) / 60. Substituting the given values into the formula, we find the angular speed to be approximately 11.55 radians/second. Then, multiply the angular speed by the radius of the blade tip to get the average speed, which turns out to be around 75.08 m/s.
b) Calculation of Average Velocity:
The average velocity over one revolution involves determining the displacement of the blade tip over a full circle and dividing it by the time taken for one revolution. By calculating the time taken for one revolution and using the formula for circumference of a circle, you can find the average velocity over one revolution. In this case, the average velocity turns out to be approximately 75.94 m/s.