Just How Fast is That Helicopter Blade Spinning?
Can you calculate the radial acceleration of a helicopter rotor blade?
The rotor blade is 3.40m long and rotates at 550rpm.
Answer:
The radial acceleration of the blade tip is 1.15 x 10³ g.
Let's break down the calculation to find the radial acceleration of the helicopter rotor blade. The length of the rotor blade is 3.40m and it rotates at a speed of 550rpm.
First, we need to calculate the angular velocity of the rotor blade in rad/s:
Angular velocity (w) = 550 rev/min * (2pi rad/1 rev) * (1 min / 60 s) = 57.6 rad/s
Next, using the formula for centripetal acceleration:
a = w² * r
Substitute the values:
a = (57.6)² * 3.4 = 1.13 x 10⁴ m/s²
Now, to express this in multiples of g, we divide by the acceleration due to gravity (g = 9.8 m/s²):
a/g = 1.13 x 10⁴ / 9.8 = 1.15 x 10³ g
Therefore, the radial acceleration of the helicopter rotor blade tip is 1.15 x 10³ g.