Question

A propeller blade, measured from the rotational axis to the tip, has a length of 1.75m. Starting from rest, the tip of the blade has a tangential acceleration of 2.47m/s². What is the angular acceleration of the propeller blade?

1) 0.71 rad/s²
2) 1.42 rad/s²
3) 2.47 rad/s²
4) 3.94 rad/s²

Answer 1

The angular acceleration of the propeller blade can be calculated using the formula ωf² - ωi² = 2αθ. Substituting the given values, we can solve for the angular acceleration α. Therefore, the angular acceleration of the propeller blade is π²f² / 1.75 rad/s².

Step-by-step explanation:

The angular acceleration of the propeller blade can be calculated using the formula:

ωf² - ωi² = 2αθ

Where ωf and ωi are the final and initial angular velocities, α is the angular acceleration, and θ is the angle through which the propeller rotates. In this case, the propeller starts from rest and rotates to a final angular velocity ωf = 2πf, where f is the frequency. The angle θ can be calculated using the formula:

θ = ωi * t + 0.5 * α * t²

Substituting the given values, we can solve for the angular acceleration α.

Using the given values:

ωi = 0 rad/s, ωf = 2πf, θ = 1.75 m

Using the first equation, we have:

α = (ωf² - ωi²) / (2θ)

Substituting the values, we get:

α = (2πf)² / (2 * 1.75)

Simplifying the equation gives:

α = π²f² / 1.75

Therefore, the angular acceleration of the propeller blade is π²f² / 1.75 rad/s².