Parallel Axis Theorem: arbitrary shape

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Question statement

{geogebra_applet('gy7gyfft', ['d_x': d_1, 'd_m': d_2])}

Give any introductory information the student needs.

			Name	Type	Generated Value

d_1	integer	9
d_2	integer	-2
A	integer	2800
Ibar	integer	2800
Ix	number	229600
Im	number	14000

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..10)random([-1,1])

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap $\bar{i}$ Engineering Accuracy with units
  Add
2. Gap $I_M$ Engineering Accuracy with units
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Gap-fill

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The area of the shape is {qty(A, 'in^2')} and its moment of inertia about the $x$ axis is {qty(Ix,'in^4')}.

Determine the centroidal moment of inertia about the $C$ – $C$ axis.

$\bar{I}_C =$ $\bar{i}$

Determine the moment of inertia about the $M$ – $M$ axis.

$I_M =$ $I_M$

Advice

Given:

$A = \var{qty(A,'in^2')}, \quad I_x = \var{qty(Ix,'in^4')}, \quad d_1 = \var{qty(abs(d_1),"in")}, \quad d_2 = \var{qty(abs(d_2),"in")}$

Find $\bar{I}_C$

$\begin{align} I &= \bar{I} + A d^2 \Rightarrow &\bar{I}_C &= I_x - A (d_1)^2 \\ && &= \var{Ix} - \var{A} (\var{abs(d_1)})^2\\ &&&= \var{qty(Ibar,'in^4')}\end{align}$

Find $I_M$

$\begin{align} I &= \bar{I} + A d^2 \Rightarrow &I_M &= \bar{I}_C + A (d_2)^2 \\ && &= \var{Ibar} + \var{A} (\var{abs(d_2)})^2\\ &&&= \var{qty(Im,'in^4')}\end{align}$

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William Haynes 3 years, 5 months ago

William Haynes 3 years, 5 months ago

William Haynes 3 years, 5 months ago

William Haynes 3 years, 5 months ago

Error in variable testing condition

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Generated value: `integer`

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Parallel Axis Theorem: arbitrary shape

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 3 years, 5 months ago

William Haynes 3 years, 5 months ago

William Haynes 3 years, 5 months ago

William Haynes 3 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`