Let l be x = 9 My M and where: M₁ = [[_ xô(x,y) dA, M₂ = [[_y6(x,y) dA_ and R R Consider the region and y= Mx M The quantities Mr and My are called the moments of the region R about the x and y axes respectively, and the quantity M is the mass of the re- gion R. 0²1?e - Sf. 8(x, y) da M =
Let l be x = 9 My M and where: M₁ = [[_ xô(x,y) dA, M₂ = [[_y6(x,y) dA_ and R R Consider the region and y= Mx M The quantities Mr and My are called the moments of the region R about the x and y axes respectively, and the quantity M is the mass of the re- gion R. 0²1?e - Sf. 8(x, y) da M =
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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Question
Transcribed Image Text:2.
Let R be a region in the xy-plane that comes with a density function d;
that is, 6 : R → R. The centre of mass of the region R is a point (x, y)
in R², where
x =
and where:
M₁ = SS₁ x8(x, y) dA, Mx
R
Let l be
M₂
M
Consider the region
and y
Mx
M
=
= y(x,y) dA and M
R
The quantities Me and My are called the moments of the region R about
the x and y axes respectively, and the quantity M is the mass of the re-
gion R.
=
-11, 41(2, 1) DA
R
R= {(x,y) √x² + y² ≤l, y ≥ 0 x>0}
and let 6(x, y) = xy√√x² + y² be a density function with domain R.
Make a sketch of R and calculate its centre of mass.
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