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.