Final answer:
The average speed of a helicopter blade tip that spins at 100 rpm and is 5.00 m from the center of rotation is 52.3 m/s. The average velocity over one revolution is 0 m/s because velocity takes into account direction, and the displacement after one revolution is zero. Rotational kinetic energy in helicopter blades is significant for their operation and safety.
Step-by-step explanation:
To calculate the average speed of the helicopter blade tip, we need to determine the distance traveled in one revolution and divide it by the time for one revolution. Since the blade spins at 100 revolutions per minute (rpm),
we can calculate the circumference of the circle made by the tip of the blade (which is one complete revolution) using the formula Circumference = 2πr, where r = 5.00 m. With the radius of the circle being 5.00 m, the circumference (distance traveled by the tip in one revolution) is 2π * 5.00 m = 31.4 m. There are 60 seconds in a minute, so the blade completes one revolution in 0.6 seconds because 60 seconds / 100 revolutions = 0.6 seconds/revolution. Therefore, the average speed of the blade tip is 31.4 m/0.6 s = 52.3 m/s.
For part (b), the average velocity of the blade tip over one revolution is 0 m/s because velocity is a vector quantity which takes into consideration the direction as well as the magnitude of speed. After one complete revolution, the blade tip returns to its starting point, thus displacement is zero and so is the average velocity over one revolution.
Helicopters store large amounts of rotational kinetic energy in their blades, which is critical for their operation. This energy must be accounted for when understanding helicopter dynamics and safety.