- #1

hitspace

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## Homework Statement

You are asked to design an airplane propleller to turn at 2400 rpm. The forward airspeed of the plane is to be 75.0 m/s, and the speed of the tips of the propeller blades through the air must not exceed 270 m/s. What is the maximum radius the propeller can have? With this radius, what is the acceleration of the propeller tip?

## Homework Equations

v = rw

alpha = omega^2 (r)

## The Attempt at a Solution

My issue with this problem is after trying to understand the explained solution. This problem is an example in my physics book.

Both the book and I convert the 2400 rpm into rad/s

(2400(2)pi)/60 = 251 rad/s

This is where I get confused. I simply divide as so, v= rw , so v/w = r

270/251 = 1.07 m

The book doesn't do this, instead it says V_tip^2 = V_plane^2 + V_tan^2 = V_plane^2 + (r^2)(w^2)

They then solve for r and get r = 1.03 vs what I got, 1.07.

What exactly are they accounting for is I think what I am trying to understand. Thanks in advance.