Engineering Mechanics: Dynamics (14th Edition)
Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 16.3, Problem 1FP

Determine its constant angular acceleration and the time required.

Chapter 16.3, Problem 1FP, Determine its constant angular acceleration and the time required.

Expert Solution & Answer
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To determine

The gear’s constant angular acceleration and the time required to achieve the angular velocity ω=30rad/s

Answer to Problem 1FP

The gear’s constant angular acceleration α to achieve the angular velocity ω=30rad/s

Is 3.58rad/s2

The time required to achieve the angular velocity ω=30rad/s is 8.38s .

Explanation of Solution

Given:

The angular acceleration α is 3rad/s2 .

Final angular velocity ω is 30rad/s .

The angular displacement of gear θ is 20rev .

Write the expression of angular displacement for gear.

θ=20rev(2πrad1rev)=40πrad

Write the equation of the angular acceleration.

α=3rad/s2

Here, angular acceleration is α .

Write the expression for the angular velocity.

ω=ω0+αct (I)

Here, angular velocity is ω , angular acceleration is αc and time is t .

Write the expression for the angular velocity.

ω2=ω02+2αc(θθ0) (II)

Here, angular velocity is ω , initial velocity is ω0 , initial revolutions is θ0 , angular acceleration is αc and revolutions is θ .

Conclusion:

Substitute   40π for θ , 0 for θ0 , 0 for ω0 and 30rad/s for ω in Equation (I).

ω2=ω02+2αc(θθ0)(30)2=(0)2+2αc[40π0]αc=3.581rad/s2

Thus, the gear’s constant angular acceleration α to achieve the angular velocity ω=30rad/s is 3.58rad/s2

Substitute 3.581rad/s2 for αc , 0 for ω0 and 30rad/s for ω in Equation (II).

ω=ω0+αct(30)=(0)+(3.581)tt=8.38s

Thus, the time required to achieve the angular velocity ω=30rad/s is 8.38s .

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Chapter 16 Solutions

Engineering Mechanics: Dynamics (14th Edition)

Ch. 16.3 - Determine the number of revolutions, the angular...Ch. 16.3 - Determine the number of revolutions it must...Ch. 16.3 - Also, find the number of revolutions of gear D to...Ch. 16.3 - Gears A, B, C, and D have radii of 15 mm, 50 mm,...Ch. 16.3 - Determine the magnitude of acceleration of point B...Ch. 16.3 - pulley A is given a constant angular acceleration...Ch. 16.3 - Starting from rest, determine the angular...Ch. 16.3 - If the engine turns pulley A at A = (20t + 40)...Ch. 16.3 - If the engine turns pulley A at A = 60 rad/s,...Ch. 16.3 - Determine the angular velocity of the disk and its...Ch. 16.3 - Determine the magnitudes of the normal and...Ch. 16.3 - Determine the magnitudes of the normal and...Ch. 16.3 - If this gear is initially turning at A = 15 rad/s,...Ch. 16.3 - If this gear is initially turning at A = 15 rad/s,...Ch. 16.3 - Determine the brushs angular velocity when t = 4...Ch. 16.3 - If this gear is initially turning at (A)0 = 20...Ch. 16.3 - Determine the magnitudes of the velocity and the n...Ch. 16.3 - 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