Explanation Calculation: Sketch the element as shown in Figure 1. Find the differential element of mass ( d m ) as shown below: m = ρ V (1) Here, ρ is density and V is volume of cylinder. Differentiate with respect to V . d m = ρ d V (2) Substitute π a 2 d x for d V in Equation (2). d m = ( π a 2 d x ) ρ = ρ π a 2 d x Find the strip element ( d I y ) about y axis as shown below: d I y = d I ¯ y + x 2 d m (3) Substitute ( 1 4 a 2 d m ) for d I ¯ y in Equation (3). d I y = ( 1 4 a 2 d m ) + x 2 d m = ( 1 4 a 2 + x 2 ) ρ π a 2 d x (4) Integrate the Equation (4) and apply the limits. d I y = ∫ d I y = ∫ − L 2 L 2 ρ π a 2 ( 1 4 a 2 + x 2 ) d x = ρ π a 2 [ 1 4 a 2 x + x 3 3 ] − L 2 L 2 = 2 ρ π a 2 [ 1 4 a 2 x + x 3 3 ] 0 L 2

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Chapter 9.5, Problem 9.119P

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Find the mass moment of inertia with respect to y axis of the right circular cylinder by using direct integration.

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Chapter 9.5, Problem 9.118P

Chapter 9.5, Problem 9.120P

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Find the mass moment of inertia with respect to y axis of the right circular cylinder by using direct integration.

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Find the mass moment of inertia with respect to y axis of the right circular cylinder by using direct integration.

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