University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2024
Views:

266

Pages:

1
Author:

Quintin Ware

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 176. (a) From sample Problem 9.11, we have at the apex A Ix = 3 ma 2 10 I y = Iz = 3 1 2  m  a + h2  5 4  Now observe that symmetry implies I xy = I yz = I zx = 0 Using Equation (9.48), the equation of the ellipsoid of inertia is then I x x2 + I y y 2 + I z z 2 = 1 or 3 3 1 3 1   ma 2 x 2 + m  a 2 + h 2  y 2 + m  a 2 + h 2  z 2 = 1 10 5 4 5 4   For the ellipsoid to be a sphere, the coefficients must be equal. Therefore, 3 3 1  ma 2 = m  a 2 + h 2  10 5 4  or a = 2 h (b) From Sample Problem 9.11, we have I x′ = I y′′ = and at the centroid C Then I y′ 3 ma 2 10 3  2 1 2 m a + h  20  4  3  2 1 2 h m a + h  + m  = I z′ = 20  4  4 = 1 m 3a 2 + 2h 2 20 ( 2 ) Now observe that symmetry implies I x′y′ = I y′z′ = I z′x′ = 0 From part a it then immediately follows that 3 1 ma 2 = m 3a 2 + 2h 2 10 20 ( ) or a = h 2 3

COSMOS Chapter 9 Solution 176

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