What is the average speed of the helicopter blade tip and its average velocity over one revolution?
The average speed of the helicopter blade tip is 3142 meters/minute. However, the average velocity over one revolution is zero because the blade tip returns to its starting position.
Calculating Average Speed:
To calculate the value of the average speed of the blade tip in the helicopter’s frame of reference, we can use the concept of circular motion, as the motion of a spinning helicopter blade is an example of circular motion. The average speed is given by the product of the distance traveled (circumference of the circle) and the frequency of rotation (revolutions per minute).
First, we calculate the circumference of the circle. The formula for the circumference (C) of a circle is 2 * pi * radius (r). With a radius of 5m, we get C = 2 * pi * 5 = 31.42m.
Next, calculate the distance traveled in one minute by multiplying the circumference by the number of revolutions per minute. We get 100 revolutions/min * 31.42m/revolution, which equals 3142 meters/minute.
Understanding Average Velocity:
For part (b) of the question, the average velocity of the blade tip over one revolution is zero. This is because velocity is a vector quantity and it depends on displacement (change in position). After one full revolution, the blade tip is back at its starting point, and therefore its displacement is zero and so is the velocity.