How Fast Does a Helicopter Blade Tip Move?
a) What is the average speed of the blade tip in the helicopter's frame of reference, in meters per second?
What is the relationship between the number of revolutions per minute and the average speed of the blade tip?
b) What is the average velocity over one revolution, in meters per second?
How does the concept of displacement affect the average velocity over one revolution?
Answer:
The average speed of the blade tip of the helicopter is 98.2 m/s, but the average velocity over one revolution is 0 m/s because the blade tip returns to its starting point.
To calculate the average speed of the blade tip, you need to multiply the distance covered in one revolution (the circumference, 2πr) by the number of revolutions per minute (rpm/60). So we have:
Speed = 2π*8.5m*(110rev/min)/60s = 98.2 m/s.
This is the average speed of the blade tip in meters per second.
The average velocity of the blade tip over one revolution, however, is 0 m/s. This is because velocity is a vector quantity, which means it has both magnitude and direction. In one revolution, the blade tip returns to its starting point. As such, the displacement (the shortest distance from the initial to the final position) is zero. Therefore, the average velocity over one revolution would be 0 m/s.