Problem 20.1 The propeller of an airplane is rotating at a constant speed ?xi, w

Question

Problem 20.1 The propeller of an airplane is rotating at a constant speed ?xi, while the plane is undergoing a turn at a constant rate ?t.

A) Determine the angular acceleration of the propeller if the turn is horizontal, i.e., ?tk.

Express your answer in terms of ?x, ?t, unit vectors i, j, and k. Use the 'vec' button to denote vectors in your answers.

B) Determine the angular acceleration of the propeller if the turn is vertical, downward, i.e., ?tj.

Express your answer in terms of ?x, ?t, unit vectors i, j, and k. Use the 'vec' button to denote vectors in your answers.

Explanation / Answer

Given that

The propeller of an airplane is rotating at a constant speed xi,

while the plane is undergoing a turn at a constant rate t.

Then the angular acceleration of the propeller if the turn is horizontal, i.e., tk.is given by

alpha =(t)k X (s)i

If we take crossproduct then we get

alpha =(st)j

b)

The angular acceleration of the propeller if the turn is vertical, downward, i.e., tj is given by

alpha =(tj)X(si)

Then from the crossproduct we get

alpha= -(st)k

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