Angular Displacement Calculation for Helicopter Rotor Blades

What is the angular displacement in radians for the operation of helicopter rotor blades spinning at a high speed of 510 rpm for 3 hours?

Angular Displacement Calculation:

The angular displacement of the blade is 576,871.2 radians

When the helicopter rotor blades spin at a high speed of 510 rpm, we need to calculate the angular displacement in radians for a 3-hour operation. First, we convert the angular speed from rpm to radian per second:

Given:

Angular speed (ω) = 510 rpm

Time of motion (t) = 3 hours

The formula to calculate angular speed in radian per second is:

ω = (510 rev/min) * (2π rad/rev) * (1 min/60 s)

ω = 53.414 rad/s

Next, we use the formula for angular displacement in radians:

θ = ωt

Substitute the values:

θ = (53.414 rad/s) * (3 hours * 60 minutes/hour * 60 seconds/minute)

θ = 576,871.2 radians

Therefore, the angular displacement of the helicopter rotor blade for a 3-hour operation at 510 rpm is 576,871.2 radians.