y=-a(x-h)² + k (-2.1, 2.2) (1, n) For the purple region bounded by a parabola with vertex at (-1, 5) and the green line, solve for: a. Area b. Centroid c. Volume when revolved 230° about the green line d. MOI and radius of gyration about the x-axis using horizontal strips. e. MOI and radius of gyration about the y-axis using vertical strips. f. MOI and radius of gyration about the z-axis
y=-a(x-h)² + k (-2.1, 2.2) (1, n) For the purple region bounded by a parabola with vertex at (-1, 5) and the green line, solve for: a. Area b. Centroid c. Volume when revolved 230° about the green line d. MOI and radius of gyration about the x-axis using horizontal strips. e. MOI and radius of gyration about the y-axis using vertical strips. f. MOI and radius of gyration about the z-axis
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter9: Moments And Products Of Inertia Of Areas
Section: Chapter Questions
Problem 9.26P: A circular region of radius R/2 is cut out from the circular region of radius R as shown. For what...
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Transcribed Image Text:For the purple region bounded by a parabola
with vertex at (-1, 5) and the green line, solve
y = -a(x – h)? + k
for:
a. Area
b. Centroid
c. Volume when revolved 230° about the green
line
(-2.1, 2.2)
d. MOI and radius of gyration about the x-axis
using horizontal strips.
e. MOI and radius of gyration about the y-axis
using vertical strips.
f. MOI and radius of gyration about the z-axis
(1, n)
Transcribed Image Text:Refer to the table for the computation of centroid and moments of inertia
Table 1. Centroids of Common Lines
Shapes
Images
Area
2r
2r
Quarter-Circular Are
Table 3. Moments of Inertia of Common Geometric Shapes
2
2r
Shapes
Images
1,
I,
Semicircular Are
r sin a
bh3
hb3
bh
Arc of Circle
2ra
Rectangle
12
a
12
Table 2. Centroids of Common Areas
Shapes
Images
Area
bh3
Triangle
36
1,=
12
h
bh
Triangular Area
3
2
4r
4r
ar
Quarter-Circular Area
Circle
1,=
Зп
3n
4
4
4
4r
Semiciroular Area
За
3h
2ah
Semiparabolic Area
ar*
8
Semicircle
5
3
4ah
0.11r
3h
8
Parabolic Area
3
За
3h
ah
1,=
16
Parabolie Spandrel
4
10
Quarter Circle
0.055r
0.055r
2r sin a
ar?
1. =
16
Circular Sector
3a
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