How to Calculate Helicopter Propeller Blade Speed?

How can we determine the speed of a point on a helicopter propeller blade given its angular acceleration and distance from the axis of rotation?

Understanding the Concept

Angular acceleration is the rate of change of angular velocity over time. In the case of a helicopter propeller blade, it experiences a constant angular acceleration of 12.5 rad/s². This means that the blade is consistently increasing its speed of rotation.

Calculating Angular Displacement

When the blade completes 12 revolutions, the total angular displacement can be calculated by multiplying the number of revolutions by (the equivalent of one full revolution in radians).

So, total angular displacement (θ) = 12 * 2π = 24π radians.

Using Kinematic Equations

Since the angular acceleration is constant, we can apply the kinematic equations to determine the time taken for the blade to complete the 12 revolutions.

The equation we can use is: θ = ω₀t + ½αt², where θ is the angular displacement, ω₀ is the initial angular velocity, α is the angular acceleration, and t is the time.

Calculating Time Taken

By substituting the known values into the equation, we can solve for the time taken. In this case, the time taken for the blade to complete the 12 revolutions is 2.4 seconds.

Determining Final Angular Velocity

Using the equation ω = ω₀ + αt, we can calculate the final angular velocity of the blade after completing the 12 revolutions. This gives us a final angular velocity of 30 rad/s.

Calculating Speed of a Point on the Blade

Finally, to find the speed of a point on the helicopter propeller blade that is 3.20 meters from the axis of rotation, we use the formula: v = r × ω, where v is the speed, r is the distance from the axis of rotation, and ω is the angular velocity.

Substituting the values, we get: speed = 3.2 * 30 = 96 m/s.

Therefore, the speed of a point on the helicopter propeller blade 3.20 m from the axis of rotation, when the blade has completed 12 revolutions, is 96 m/s.

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