Explanation Calculation: Find the position vector of OA . O A → = 3 2 a i − 3 a j + 3 a k Find the magnitude of O A → using the relation as shown below: d O A = ( 3 2 a ) 2 + ( − 3 a ) 2 + ( 3 a 2 ) = ( 9 4 a 2 ) + ( 9 a 2 ) + ( 9 a 2 ) = 3 a 1 + 4 + 4 4 = 3 a 9 4 = 3 a 3 2 d O A = 9 a 2 Find the magnitude of λ O A as shown below: λ O A = 1 9 2 a ( 3 2 a i − 3 a j+3 a k ) = 2 9 a ( 3 2 a i − 3 a j+3 a k ) = 1 3 ( i − 2 j + 2 a k ) For a rectangular coordinate system with origin at point A and axes aligned with the given x , y , z axes. Refer to Figure 9.28 in section,”9.5E Moments of inertia of composite bodies” in the textbook. Express the moment of inertia about x and z axis of circular cone as shown below: I x = I z = 3 5 m [ 1 4 a 2 + ( 3 a ) 2 ] = 3 5 m [ 1 4 a 2 + 9 a 2 ] = 3 5 m [ 37 a 2 4 a 2 ] = 111 20 m a 2 Express the moment of inertia about y axis of circular cone as shown below: I y = 3 10 m a 2 As the symmetry implies I x y = I y z = I z x = 0 . Refer to Equation 9.46 in section, “9

Vector Mechanics for Engineers: Statics and Dynamics

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ISBN: 9781259977251

Author: BEER

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Chapter 9.6, Problem 9.163P

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Find the mass moment of inertia of the cone with respect to the line joining the origin O and point A.

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Chapter 9.6, Problem 9.162P

Chapter 9.6, Problem 9.164P

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1) Solve and show which is converage or diyverage a = 2+(0.1)" 3 16) a = n 1-2n 2) a = In n 1+2n 17) a = n 1-5n4 3) an = n* +8n³ 18) a =√4"n n² -2n+1 n! 20) a = 4) a₁ = 10 n-1 (Ina) 5) a=1+(-1)" 21) a= 6) a 7) an = * = (12+) (1-1) 2n (-1)+1 2n-1 3n+1 22) a= 3n-1 x" 23) a= .x>0 2n+1 2n 3"x6" 8) a = 24) a = n+1 π 9) a = sin 2 sin n 10) an = n + 2 x n! 25) a = tanh(n) n² 1 26) a = -sin- 2n-1 27) a = tan(n) n n 11) a = 2" 12) a = n 13) a = 8/ +=(1+2)" 14) a = 15) a = √10n In(n+1) 29) a = n 30) an-√n²-1 1 28) a = + √2" (In n)200 n 31) a=- = 1 dx nix

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Find the mass moment of inertia of the cone with respect to the line joining the origin O and point A .

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Find the mass moment of inertia of the cone with respect to the line joining the origin O and point A.

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