Explanation Given data: The length of the shaft is 4 feet and the diameter of the shaft is 2 in., which is equal to 2 × 0.0833 ft = 0.167 ft using the condition 1 in . = 0.0833 ft . Therefore, the radius of the shaft ( R ) is 0.167 ft 2 = 0.0833 ft . The angular speed of shaft is 100 rpm, which is equal to 100 × 9.549 = 10.47 rad/s . Formula used: Consider the expression for the density. density = mass volume (1) Write the expression for the volume of the shaft. volume = π 4 d 2 ( length ) (2) Consider the expression for the mass moment of inertia. I z − z = 1 2 m R 2 (3) Here, m is mass, and R is radius of the shaft. Consider the expression for the rotational kinetic energy. Rotational kinetic energy = 1 2 I ω 2 (4) Calculation: Refer to Table 9.1 in the textbook. The value of density for steel is 7860 kg m 3 . Substitute 4 ft for length and 0.167 feet for d in equation (2), volume = π 4 ( 0.167 ft ) 2 ( 4 ft ) = 0.088 ft 3 Substitute 0.088 ft 3 for volume and 7860 kg m 3 for density in equation (1), 7860 kg m 3 = mass 0.088 ft 3 7860 ( 0.00194 slugs ft 3 ) = mass 0.088 ft 3 { ∴ 1 kg m 3 = 0.00194 slugs ft 3 } 15.2 slugs ft 3 = mass 0.088 ft 3 mass = 1.34 slugs Substitute 1.34 slugs for m and 0.0833 feet for R in equation (3), I z − z = 1 2 ( 1.34 slugs ) ( 0.0833 ft ) 2 = 0.0046 slugs ⋅ ft 2 Convert the unit from slugs ⋅ ft 2 to lbm ⋅ ft 2 . I z − z = 0.0046 slugs ⋅ ft 2 = ( 0.0046 ) ( 32.174 lbm ⋅ ft 2 ) [ ∴ 1 slugs = 32

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

5th Edition

ISBN: 9781305084766

Author: Saeed Moaveni

Publisher: Cengage Learning

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Unit Conversion

Standard units are also called SI units. SI units are used for measuring a physical quantity satisfying certain conditions. There are two types of units: fundamental units and derived units. Fundamental units are physical quantities that are independent,…

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Chapter 9, Problem 32P

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Find the rotational kinetic energy of the steel shaft.

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Chapter 9, Problem 31P

Chapter 9, Problem 33P

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Chapter 9 Solutions

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

Ch. 9.3 - Prob. 1BYG Ch. 9.3 - Prob. 2BYG Ch. 9.3 - Prob. 3BYG Ch. 9.3 - Prob. BYGV Ch. 9.6 - Prob. 1BYG Ch. 9.6 - Prob. 2BYG Ch. 9.6 - Prob. 3BYG Ch. 9.6 - Prob. BYGV Ch. 9 - Prob. 1P Ch. 9 - Prob. 2P

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Find the rotational kinetic energy of the steel shaft.

Solution Summary: The author calculates the rotational kinetic energy of the steel shaft using the formula in Table 9.1 in the book.

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Find the rotational kinetic energy of the steel shaft.

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Chapter 9 Solutions