Go Back   Physics Help Forum > Lobby > New Users

New Users New to PHF? Post up here and introduce yourself!

Like Tree1Likes
  • 1 Post By ChipB
Reply
 
LinkBack Thread Tools Display Modes
Old Dec 1st 2016, 09:38 PM   #1
Junior Member
 
Join Date: Dec 2016
Posts: 2
Unhappy moments of inertia

There are two questions about the moments of inertia, but I am lack of the knowledge of calculus. Could anybody help me please?

1. Determine the moments of inertia of the shaded area shown with respect to

the x and y axes.





2. Determine the polar moments of inertia and the polar radius of gyration of the shaded area shown with respect to Point P.

Sylar is offline   Reply With Quote
Old Dec 1st 2016, 09:41 PM   #2
Junior Member
 
Join Date: Dec 2016
Posts: 2
I am sorry


this picture should be no.2


and this one should be no.1
Sylar is offline   Reply With Quote
Old Dec 2nd 2016, 06:17 AM   #3
Physics Team
 
ChipB's Avatar
 
Join Date: Jun 2010
Location: Morristown, NJ USA
Posts: 2,347
I would assume that you have a list of formulas of moments of inertia for various geometric shapes, perhaps in your text or in class notes, correct? You don't need to know calculus if you have such a list - just apply the formulas adding and subtracting shapes as required. For example, for the second problem (the one that asks about moment of inertia about point P), you can consider the shaded area as a large rectangle of width 4a and height 2a, with a piece missing of width 2a and height a. The formula for moment of inertia about a point on the edge of a rectangle is m/12(4h^2 + w^2) -- more on this below; use this to calculate the moment of inertia of the large rectangle then subtract the moment of inertia of the missing piece.

A handy thing to remember is that if you know the moment of inertia about the centroid of a shape, you can determine the moment of inertia about another point P' which is distance d away by using the formula

$\displaystyle I_{P'} = I_P + md^2$

where 'm' is the mass of the shape in question. So, if your book does not have the formula for moment of inertia about a point on the edge of a rectangle, but does have it for the center of the rectangle, you can determine the proper equation as follows:

$\displaystyle I_{edge} = I_{center} + md^2$

The formula for I_center is (m/12)(h^2+m^2), so for a point on the edge you have:

$\displaystyle I_{edge} = \frac m {12} (h^2 + w^2) + m(\frac h 2)^2 = \frac m {12} (4h^2 + w^2)$

Hope this helps.
topsquark likes this.

Last edited by ChipB; Dec 2nd 2016 at 06:30 AM.
ChipB is offline   Reply With Quote
Reply

  Physics Help Forum > Lobby > New Users

Tags
cmoments, inertia, moments



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
Moments Help! electrogeek Equilibrium and Elasticity 6 Nov 8th 2016 07:58 AM
determine the moments of inertia about the horizontal and vertical axis ling233 Kinematics and Dynamics 0 Nov 26th 2015 10:40 PM
Difficulty with Center of Mass and Moments of Inertia brin Kinematics and Dynamics 0 Nov 21st 2015 11:49 AM
3D Moments vishak95 Kinematics and Dynamics 1 Mar 14th 2013 08:57 AM
Moments ManyArrows Kinematics and Dynamics 2 May 5th 2009 03:59 PM


Facebook Twitter Google+ RSS Feed