A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. What is the radial acceleration of the blade tip expressed as a multiple of g?

Verified step by step guidance

1. First, understand that radial acceleration, also known as centripetal acceleration, is given by the formula: $a={\omega }^{2}r$, where $\omega$ is the angular velocity in radians per second and $r$ is the radius.
2. Convert the angular velocity from revolutions per minute to radians per second. Use the conversion factor: $1\mathrm{rev}=2\pi \mathrm{rad}$ and $1\min =60s$.
3. Calculate the angular velocity $\omega$ using the formula: $\omega =550\times 2\pi /60$.
4. Substitute the values of $\omega$ and $r$ (which is 3.40 m) into the radial acceleration formula: $a={\omega }^2\times 3.40$.
5. Finally, express the radial acceleration as a multiple of $g$ (where $g=9.81\mathrm{m/s}²$) by dividing the calculated radial acceleration by $g$.

Key Concepts

Centripetal Acceleration

Centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed towards the center of the circle. It is calculated using the formula a_c = ω²r, where ω is the angular velocity and r is the radius of the circle. This concept is crucial for determining the radial acceleration of the helicopter blade tip.

Angular Velocity

Angular velocity is a measure of how quickly an object rotates around a central point, expressed in radians per second. It is calculated by converting revolutions per minute (rev/min) into radians per second using the formula ω = 2π × (rev/min) / 60. Understanding angular velocity is essential for calculating centripetal acceleration.

Gravitational Acceleration

Gravitational acceleration, denoted as g, is the acceleration due to Earth's gravity, approximately 9.81 m/s². When expressing radial acceleration as a multiple of g, it involves dividing the calculated centripetal acceleration by g to find how many times greater the radial acceleration is compared to gravitational acceleration.