{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

sec8_3

# sec8_3 - (1 3 x 2 y = 6 y = 0 and x = 0(2 y = 1/x y = 0 x =...

This preview shows pages 1–3. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Section 8.3 Applications to Physics and Engineering 2 Definition 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 = b a f ( x ) dx.
Section 8.3 Applications to Physics and Engineering 3 2. Examples Example 2.1. Find the centroid of the region bounded by the curves,
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online