Applied Maths - Moments of Inertia

Prowetod

I was looking at skoool.ie and I noticed a proof of inertia formula that can come up and my class has not covered.

" Annulus, about centre, perpendicular to its plane: 1/2m(R^2+r^2)"
http://www.skoool.ie/skoool/examcentre_sc.asp?id=2595

Greatly appreciate if someone could go through it.

MathsManiac

An annulus is the region between two circles. (That is, a disc with a smaller disc cut out from the middle.)

So, if you can do a disc, you should be able to do an annulus. It's just a matter of integrating from r to R instead of 0 to R, and altering the expression for mass per unit area.

Prowetod

Ah ok, I will try that.
Thanks.

newie

Lads there is a smart bunch here and Im looking for a second opinion on a question, Ive a formula:

TP = 3.14
(Wn ×√(1-ε^2 ))

and I want to get the formula reading Wn = , i.e I need to find a value for Wn and I have TP and the rest. I think Im right but want a second opinion.

Delphi91

newie wrote: »

Lads there is a smart bunch here and Im looking for a second opinion on a question, Ive a formula:

TP = 3.14
(Wn ×√(1-ε^2 ))

and I want to get the formula reading Wn = , i.e I need to find a value for Wn and I have TP and the rest. I think Im right but want a second opinion.

Swap the TP and the Wn and that gives you the amended equation.

newie

was thinking that was it thanks. Also if you could how do I get the roots of this equation.


8/ s(1.5s +2)

x1= ?
x2= ?