Explanation Given information: The weight ( W ) of the flywheel is 85 lb. The period ( τ n ) of small oscillation is 1.26 sec. Assuming the acceleration due to gravity ( g ) is 32.2 ft/s 2 . Calculation: Show the position of the flywheel as in Figure (1). Calculate the mass ( m ) using the relation: m = W g Substitute 85 lb for W and 32.2 ft/s 2 for g . m = 85 32.2 = 2.6398 lb ⋅ s 2 / ft Calculate the radius ( r ) using the relation: r = d 2 Substitute 14 in . for d . r = 14 in . 2 = 7 in . × 1 ft 12 in . = 0.583 ft For position 1: Write the expression for kinetic energy ( T 1 ) : T 1 = 1 2 I 0 θ ˙ m 2 Write the expression for potential energy ( V 1 ) : V 1 = 0 For position 2. Write the expression displacement ( h ): h = r ( 1 − cos θ m ) ( ∵ ( 1 − cos θ m ) = 2 sin 2 θ m 2 ) = r ( 2 sin 2 θ m 2 ) Here, θ ˙ m is maximum angular velocity. For small oscillation sin θ ≈ θ . h = r θ m 2 2 Write the expression for kinetic energy ( T 2 ) : T 2 = 0 Write the expression for potential energy ( V 2 ) : V 2 = m g h Substitute r θ m 2 2 for h . V 2 = m g r θ m 2 2 Write the expression for maximum angular velocity ( θ ˙ m ) : θ ˙ m = ω n θ m Expression for conservation of energy: T 1 + V 1 = T 2 + V 2 Substitute 1 2 I 0 θ ˙ m 2 for T 1 , 0 for V 1 , 0 for T 2 , and m g r θ m 2 2 for V 2

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 19.3, Problem 19.73P

To determine

The centroidal moment of inertia (I¯) of the flywheel.

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Chapter 19.3, Problem 19.72P

Chapter 19.3, Problem 19.74P

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Chapter 19 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.2P Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - Prob. 19.7P Ch. 19.1 - Prob. 19.8P Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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The centroidal moment of inertia ( I ¯ ) of the flywheel.

Solution Summary: The author calculates the centroidal moment of inertia of the flywheel using the relation: m=Wg.

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The centroidal moment of inertia (I¯) of the flywheel.

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Chapter 19 Solutions