An airplane sitting on a grassy field has a single propeller consisting of 3 identical blades, as shown in the diagram. Each blade has mass M, = 20 kg and length L = 0.8 m. The mass of each blade is not evenly distributed, so that the center of mass is located e= 0.3 m from the outer end of the blade. The moment of inertia of each blade about its center of mass is Iem =2 kg m². a) The propeller is initially at rest. The pilot then starts the engine and after 5 s the propeller is rotating at o = 30 radians/s. What is the magnitude of the angular acceleration a during that time assuming the angular acceleration is constant? blade b) What is the moment of inertia of the entire propeller about its axis of rotation? C.m. c) What is the magnitude of the net torque on the propeller during the initial 5 second period? blade d) At t = 5 s, when the propeller is spinning with angular velocity o = 30 radians/s, what is the speed of the outer tip of each blade of the propeller? C.m. -C.m. blade

An airplane sitting on a grassy field has a single propeller consisting of 3 identical blades, as shown in the diagram. Each blade has mass M, = 20 kg and length L = 0.8 m. The mass of each blade is not evenly distributed, so that the center of mass is located e= 0.3 m from the outer end of the blade. The moment of inertia of each blade about its center of mass is Iem =2 kg m². a) The propeller is initially at rest. The pilot then starts the engine and after 5 s the propeller is rotating at o = 30 radians/s. What is the magnitude of the angular acceleration a during that time assuming the angular acceleration is constant? blade b) What is the moment of inertia of the entire propeller about its axis of rotation? C.m. c) What is the magnitude of the net torque on the propeller during the initial 5 second period? blade d) At t = 5 s, when the propeller is spinning with angular velocity o = 30 radians/s, what is the speed of the outer tip of each blade of the propeller? C.m. -C.m. blade

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.40P

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PM1: please answer question and explain each step with reasoning

An airplane sitting on a grassy field has a single propeller consisting of 3 identical blades, as shown in the diagram.
Each blade has mass M, = 20 kg and length L = 0.8 m. The mass of each blade is not evenly distributed, so that the
center of mass is located ( = 0.3 m from the outer end of the blade. The moment of inertia of each blade about its
center of mass is Iem = 2 kg m².
a) The propeller is initially at rest. The pilot then starts the engine and after 5 s the propeller is rotating at o = 30
radians/s. What is the magnitude of the angular acceleration a during that time assuming the angular
acceleration is constant?
blade
b) What is the moment of inertia of the
entire propeller about its axis of
rotation?
C.m.
c) What is the magnitude of the net torque
on the propeller during the initial 5
second period?
blade
d) At t = 5 s, when the propeller is spinning
with angular velocity o = 30 radians/s,
what is the speed of the outer tip of each
blade of the propeller?
-c.m.
C.m.
10.
blade

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