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Ex1: Find the moment of inertia about the x-axis of a thin plate bounded by the curve x = y? and x = 2y – y? if its density at the point (x.y) is 8(x, y) = y + 1 Solution: 1 x = 2y - y2 (0,2) x = y? (1,1) (0,0) To find points of intersections: y? = 2y – y? 2y2 – 2y = 0 y? – y = 0 y(y – 1) = 0 y = 0 then x = 0 y = 1 then x = 1 Now to find moment of inertia: I = fe y²6(x,y)dxdy = , S yv + 1)dxdy = fo* + y*)[x] dy = f,v³ + y²)(2y – y² - y²)dy = fo³ + y?)2y – y²)dy = 2 f,y* – y³ – y³ – y*)dy %3D

Ex1: Find the moment of inertia about the x-axis of a thin plate bounded by the curve x = y? and x = 2y – y? if its density at the point (x.y) is 8(x, y) = y + 1 Solution: 1 x = 2y - y2 (0,2) x = y? (1,1) (0,0) To find points of intersections: y? = 2y – y? 2y2 – 2y = 0 y? – y = 0 y(y – 1) = 0 y = 0 then x = 0 y = 1 then x = 1 Now to find moment of inertia: I = fe y²6(x,y)dxdy = , S yv + 1)dxdy = fo* + y*)[x] dy = f,v³ + y²)(2y – y² - y²)dy = fo³ + y?)2y – y²)dy = 2 f,y* – y³ – y³ – y*)dy %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Ex1: Find the moment of inertia about the x-axis of a thin plate bounded by the curve x = y? and x = 2y - y? if its density at the point (x.y) is 8(x, y) = y + 1 Solution: + x = 2y – y? (0,2) x = y? (1,1) (0,0) To find points of intersections: y? = 2y - y2 2y? – 2y = 0 y? – y = 0 y(y - 1) = 0 y = 0 then x = 0 y = 1 then x = 1 Now to find moment of inertia: Iz = Sa y²8(x,y)dxdy = , yv + 1)dxdy Jy2 = 3 + y*)[xl; dy =, t )(2y- y - y²)dy = S,v³ + y²)2Cy – y²)dy = 2 f,v* – y5 – y? – y*)dy 11 Multiple tegral H.W Find Iy, I,, Rx, Ry, Ro,X and y
Transcribed Image Text:Ex1: Find the moment of inertia about the x-axis of a thin plate bounded by the curve x = y? and x = 2y - y? if its density at the point (x.y) is 8(x, y) = y + 1 Solution: + x = 2y – y? (0,2) x = y? (1,1) (0,0) To find points of intersections: y? = 2y - y2 2y? – 2y = 0 y? – y = 0 y(y - 1) = 0 y = 0 then x = 0 y = 1 then x = 1 Now to find moment of inertia: Iz = Sa y²8(x,y)dxdy = , yv + 1)dxdy Jy2 = 3 + y*)[xl; dy =, t )(2y- y - y²)dy = S,v³ + y²)2Cy – y²)dy = 2 f,v* – y5 – y? – y*)dy 11 Multiple tegral H.W Find Iy, I,, Rx, Ry, Ro,X and y
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