Question

Moment of Inertia for different Shapes (a) Rectangle $A = ab$ $I_x = \frac{1}{12}ba^3$ $I_y = \frac{1}{12}ab^3$ $I_{xy} = 0$ (b) Circle $A = \pi r^2$ $I_x = I_y = \frac{\pi}{4}r^4$ $I_{xy} = 0$ (c) Semicircle $A = \frac{\pi}{2}r^2$ $I_x = 0.1098\pi r^4$ $I_y = 0.3927\pi r^4$ $I_{xy} = 0$ (d) Triangle $A = \frac{1}{2}bh$ $I_x = \frac{bh^3}{36}$ $I_y = \frac{b^3h}{72}(b - 2xh)$ $I_{xy} = 0$ (e) Quarter Circle $A = \frac{\pi}{4}r^2$ $I_x = I_y = 0.05488\pi r^4$ $I_{xy} = -0.016478\pi r^4$

          Moment of Inertia for different Shapes
(a) Rectangle
$A = ab$
$I_x = \frac{1}{12}ba^3$
$I_y = \frac{1}{12}ab^3$
$I_{xy} = 0$
(b) Circle
$A = \pi r^2$
$I_x = I_y = \frac{\pi}{4}r^4$
$I_{xy} = 0$
(c) Semicircle
$A = \frac{\pi}{2}r^2$
$I_x = 0.1098\pi r^4$
$I_y = 0.3927\pi r^4$
$I_{xy} = 0$
(d) Triangle
$A = \frac{1}{2}bh$
$I_x = \frac{bh^3}{36}$
$I_y = \frac{b^3h}{72}(b - 2xh)$
$I_{xy} = 0$
(e) Quarter Circle
$A = \frac{\pi}{4}r^2$
$I_x = I_y = 0.05488\pi r^4$
$I_{xy} = -0.016478\pi r^4$

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Moment of Inertia for different Shapes
(a) Rectangle
A = ab
Ix = (1)/(12)ba^3
Iy = (1)/(12)ab^3
Ixy = 0
(b) Circle
A = π r^2
Ix = Iy = (π)/(4)r^4
Ixy = 0
(c) Semicircle
A = (π)/(2)r^2
Ix = 0.1098π r^4
Iy = 0.3927π r^4
Ixy = 0
(d) Triangle
A = (1)/(2)bh
Ix = (bh^3)/(36)
Iy = (b^3h)/(72)(b - 2xh)
Ixy = 0
(e) Quarter Circle
A = (π)/(4)r^2
Ix = Iy = 0.05488π r^4
Ixy = -0.016478π r^4

Added by Paul P.

Physics for Scientist and Engineers: A Strategic Approach

Randall Knight 2nd Edition

Chapter 12

Instant Answer

Solved by Expert Anand Jangid

Step 1

- Rectangle: Ix = (1/12)bh³, Iy = (1/12)hb³, Ixy = 0 - Circle: I = (π/4)R⁴, Ixy = 0 - Semicircle: I = (1/8)πR⁴, Ixy = 0 - Triangle: I = (b³h)/36, Ixy = (b²h²)/72 + bh³/36 - Right triangle (last shape): Ix = bh³/36, Iy = hb³/36, Ixy = -b²h²/72 Show more…

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Please find the moment and inertia of all the objects and prove all the equations which are given with the figure. Find the moment of inertia of all the figures given. Moment of Inertia for different Shapes = We 1-1-# 1-0 1-0 Kal lactargle Cc 4-17 = 0.1098 = 0.3927 T4 + 0 4-90 1b-2 b+d- e Semicc a Tange = -0.05488 = -0.01647

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