Question

The propeller of a World War II fighter plane is 2.30 m in diameter and spins at 1200 rev/min. What is the centripetal acceleration of the propeller tip? Calculate it in meters per second squared and convert to multiples of g.

Answer 1

Answer:

Ac = 36320 m/s^2 = 3702 g

Explanation:

First let's find the linear velocity of the propeller tip.

The angular velocity is 1200 rev/min, which is 20 rev/s

One rev is 2*pi radians, so 20 rev/sec = 40*pi rad/s

To find linear velocity, we multiply the angular velocity by the radius, so:

V = 40*pi * 2.3 = 92*pi m/s

The centripetal acceleration is given by Ac = V^2/r, being r the radius. So:

Ac = (92*pi)^2/2.3 = 36320 m/s^2

If g is the gravity acceleration = 9.81 m/s^2, we can find Ac in multiples of g by dividing their values:

Ac = 36320/9.81 = 3702 g