Explanation Given information: The width ( b ) of circular cylinder is 1 2 h . Calculation : Sketch the conical surface as shown in Figure 1. Refer to Figure 1. Express the mass of the cylinder as shown below: m cy1 = ρ π a 2 h Express the mass of the cone as shown below: m cone = 1 3 ρ π a 2 h 2 = 1 6 π ρ a 2 h Express the moment of inertia of cylinder as shown below: I cy1 = 1 2 m cy 1 a 2 (1) Substitute ρ π a 2 h for m cy1 in Equation (1). I cy1 = 1 2 ( ρ π a 2 h ) a 2 = 1 2 ( ρ π a 4 h ) Express the moment of inertia of cone as shown below: I cone = 3 10 m cone a 2 (2) Substitute 1 6 π ρ a 2 h for m cone in Equation (2). I cone = 3 10 ( 1 6 π ρ a 2 h ) a 2 = 3 10 ( 1 6 π ρ a 4 h ) = 3 60 π ρ a 4 h = 1 20 π ρ a 4 h Find the mass of entire machine part as shown below: m = m cy1 − m cone (3) Here, m cy1 is mass of cylinder part and m cone is mass of conical part. Substitute ρ π a 2 h for m cy1 and 1 6 π ρ a 2 h for m cone in Equation (3). m = ρ π a 2 h − 1 6 π ρ a 2 h = ρ π a 2 h − 1 6 ρ π a 2 h = ρ π a 2 h ( 1 − 1 6 ) = ρ π a 2 h ( 5 6 ) m = 5 6 ρ π a 2 h Find the moment of inertia about y axis as shown below: I y = I cy1 − I cone (4) Here, I cy1 is moment of inertia of cylindrical section and I cone is moment of inertia of cone section

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 9.5, Problem 9.129P

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Find the mass moment of inertia and radius of gyration of the machine part with respect to y axis.

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Chapter 9.5, Problem 9.128P

Chapter 9.5, Problem 9.130P

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Vector Mechanics for Engineers: Statics and Dynamics

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Find the mass moment of inertia and radius of gyration of the machine part with respect to y axis.

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Find the mass moment of inertia and radius of gyration of the machine part with respect to y axis.

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