Moment of Inertia: rectangles

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Question statement

{geogebra_applet('b3fxtwx6',[['A',A],['B',B]])}

Use the formula below for the moment of inertia of a rectangle about an axis passing through its base to find the moment of inertia of the composite shape about both the x- and y- axes. Grid units are [{unit}].

$I = \dfrac{b h^3}{3}$

Give any introductory information the student needs.

			Name	Type	Generated Value

b_1	number	6
h_1	number	9
b_2	number	4
h_2	number	3
b_3	number	3
h_3	number	10
b_4	number	6
h_4	number	6
Ix	number	1494
removed_x	boolean	false
removed_y	boolean	false
Iy	number	1432

			Name	Type	Generated Value

A	vector	vector(6,9)
B	vector	vector(10,3)
add	boolean	true
unit	string	cm
units	quantity	quantity(1, "cm^4")

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xxxxxxxxxx
 
A[0]

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1. Gap $I_x$ Engineering Accuracy with units
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2. Gap $I_y$ Engineering Accuracy with units
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$I_x$ = $I_x$ $\qquad I_y = $ $I_y$

Advice

To find $I_x$ consider the shape to be made of a $ (\var{b_1} \times \var{h_1})$ rectangle and a $(\var{b_2} \times \var{h_2})$ {if(removed_x,'removed','')} rectangle.

$ \quad I_x = \dfrac{ (\var{b_1}) (\var{h_1})^3}{3} \, \var{if(removed_x, '–' , '+')} \,\dfrac{ (\var{b_2}) (\var{h_2})^3}{3} = \var{siground(ix units, 4)} \\$

To find $I_y$ consider the shape to be made of a $ (\var{b_3} \times \var{h_3})$ rectangle and a $(\var{b_4} \times \var{h_4})$ {if(removed_y,'removed','')} rectangle.

$\quad I_y = \dfrac{ (\var{b_3}) (\var{h_3})^3}{3} \, \var{if(removed_y, '–' , '+')} \,\dfrac{ (\var{b_4}) (\var{h_4})^3}{3}= \var{siground(Iy units,4)}$

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This question is used in the following exams:

Chapter 10 Exercises by Michael Proudman in Engineering Statics.
23. Moment of Inertia by Michael Proudman in Engineering Statics.
Chapter 10 Exercises by William Haynes in Engineering Statics.
23. Moment of Inertia by William Haynes in Engineering Statics.

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William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

Error in variable testing condition

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Generated value: `number`

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Moment of Inertia: rectangles

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`