Question

The propeller of a World War II fighter plane is 2.30 m in diameter.

(a) What is its angular velocity in radians per second if it spins at 1200 rev/min?

(b) What is the linear speed of its tip at this angular velocity if the plane is stationary on the tarmac?

(c) What is the centripetal acceleration of the propeller tip under these conditions? Calculate it in meters per second squared and convert to multiples of g .

(d) What is the acceleration of the propeller tip when the plane is taxiing forward from rest to 10mph over 2 seconds? Assume the same angular velocity for the propeller.

Answer 1

a)

w = 1200* 2* 3.14 / 60

w = 125.6 rad/s

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b)

v = rw =125.6* 2.3 = 288.88 m/s

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c)

a = r w^2 = 2.3* 125.6^2 = 36283.33 m/s^2

in accordance to acceleration due to gravity

a = 36283.33 / 9.8 g = 3702.38 m/s^2

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d)

tangential acceleration

at = ( 10* 1.6* 5 / 18) / 2 = 2.22 m/s^2

centripetal acceleration

ac = 36283.33 m/s^2

net acceleration

a ^2 = ac^2 + at^2

a = 36283.33 m/s^2

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