Think About It The center of mass of a solid of constant density is shown in the figure. In Exercises 43-46, make a conjecture about how the center of mass ( x ¯ , y ¯ , z ¯ ) will change for the nonconstant density ρ ( x , y , z ) . Explain. (Make your conjecture without performing any calculations.) ρ ( x , y , z ) = k x
Solution Summary: The author explains that the center of mass of a solid of constant density is (x,y,z)=kx.
Think About It The center of mass of a solid of constant density is shown in the figure. In Exercises 43-46, make a conjecture about how the center of mass
(
x
¯
,
y
¯
,
z
¯
)
will change for the nonconstant density
ρ
(
x
,
y
,
z
)
. Explain. (Make your conjecture without performing any calculations.)
Plate with variable density Find the mass and first momentsabout the coordinate axes of a thin square plate bounded by thelines x = ±1, y = ±1 in the xy-plane if the density is d(x, y) =x2 + y2 + 1/3.
Finding a center of mass Find the center of mass of a thin plateof density d = 3 bounded by the lines x = 0, y = x, and the parabolay = 2 - x2 in the first quadrant.
A lamina occupies the part of the disk x2 + y2 ≤ 16 in the first quadrant. Find the center of mass of the lamina if the density at any point is proportional to the square of its distance from the origin.
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY