sec8_3

sec8_3 - (1) 3 x + 2 y = 6 , y = 0 and x = 0 . (2) y = 1 /x...

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8.3 Applications to Physics and Engineering 1. Center of Mass m 1 d 1 = m 2 d 2 ¯ x = m 1 x 1 + m 2 x 2 m 1 + m 2 1
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Section 8.3 Applications to Physics and Engineering 2 Defnition 1.1. (1) Moment of the system about the origin, M = n i =1 m i x i On xy plane, (2) Moment of the system about the y -axis, M y = n i =1 m i x i (3) Moment of the system about the x -axis, M x = n i =1 m i y i Theorem 1.1. Moments of a region R : M y = ρ ± b a xf ( x ) dx M x = ρ ± b a 1 2 [ f ( x )] 2 dx Theorem 1.2. Center of Mass (Centroid): ¯ x = 1 A ± b a xf ( x ) dx ¯ y = 1 A ± b a 1 2 [ f ( x )] 2 dx where A = ² b a f ( x ) dx.
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Section 8.3 Applications to Physics and Engineering 3 2. Examples Example 2.1. Find the centroid of the region bounded by the curves,
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Unformatted text preview: (1) 3 x + 2 y = 6 , y = 0 and x = 0 . (2) y = 1 /x , y = 0 , x = 1 and x = 2 . Theorem 2.1. If the region R lies between two curves y = f ( x ) and y = g ( x ) , where f ( x ) g ( x ) , then the centroid is x = 1 A b a x [ f ( x )-g ( x )] dx y = 1 A b a 1 2 { [ f ( x )] 2-[ g ( x )] 2 } dx Example 2.2. Find the centroid of the region bounded by y = x + 2 and y = x 2 ....
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This note was uploaded on 03/14/2011 for the course MAC 2312 taught by Professor Zhang during the Fall '07 term at FSU.

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sec8_3 - (1) 3 x + 2 y = 6 , y = 0 and x = 0 . (2) y = 1 /x...

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