What is the moment of inertia of a disc and rectangular plate system?

[dreamz25]

q) A disc of mass 'm' and radius 'R' is attached to a rectangular plate of the same mass, breadth R and elngth 2R as shown in the figure. Find the moment of inertia of this system about the axis XX' passing through the centre of the disc and along the plane.

http://encodable.com/uploaddemo/files/picasa.png

please help me out...!

 

[Simon Bridge]

Well it's the sum of the moments separately ... I think the parallel axis theorem is your friend here. It is a good idea to show some attempt at working it out if only to show us how you are thinking about the problem.

 

[dreamz25]

what i did was found the moment of inertia of the rectangular plate about the axis perpendicular to it and passing through the com
i.e, I1 = M(2R^2 + R^2)/12 = 5{MR^2}/12
Again,
I2 = M.I of the circular disc about the axis passing through its centre and perpendicular to it + I1 + M(d)^2 where d is the distance between them

so using it the T.I = MR^2/2 + 5MR^2/12 + M(3R/2)^2
= 19/6 MR^2
So, M.I about the axis passing through the centre and in the plane of the disc = 19/12 MR^2

but its 31/12 MR^2 which the book says...
so please help...
and yea i m a beginner.. :P

 

[tiny-tim]

welcome to pf!

hi dreamz25! welcome to pf!

oooh, wrong axis! …

Find the moment of inertia of this system about the axis XX' passing through the centre of the disc and along the plane.

… the axis is in the plane of the diagram

 

[Simon Bridge]

The one he want's is not, in so many words, in this list:
http://en.wikipedia.org/wiki/List_of_moments_of_inertia
... derive it from the result for a cuboid?

 

[tiny-tim]

no, from the perpendicular axis theorem for moment of inertia

 

[dreamz25]

thankyou sir...
but can u please work it out...!
m not getting what u want to say actually (

 

[Simon Bridge]

@tiny-tim: Doesn't it give the same result?
@dreamz25: we are not supposed to do your work for you - working out the result yourself is part of the homework.
Try looking up the terms used and following the links supplied.

It looks like you know the formulae but don't understand them.
You found the moment of inertia for the plate for an axis perpendicular to it, but you need the axis along it's length.
Then apply parallel axis theorem.

Add to the moment of inertia for a disk, same problem - you need an axis through the center but in the plane of the disk, not perpendicular to it.
Look at the diagram you have and compare with the ones accompanying the formulae you used.

 

[tiny-tim]

m not getting what u want to say actually (

the formula you used is for the moment of inertia about an axis perpendicular to the plane of the disc or plate …

but the question asks about an axis parallel to (in) the plane of the disc or plate

 

[dreamz25]

That's what my problem is...?
Perpendicular axis theorem says
I = Ix + Iy
but if it would have been a square then it was easy to calculate M.I of the plate about the axis in the plane of it...
but i don't know how to do it for the rectangular plate...?
Please atleast give me some source or proper concept...!
Afterall i showed whatever i could..!

 

[dreamz25]

Once we know the M.I of the rec. plate about the axis parallel to XX' then its easy to apply the parallel axis theorem and kill the question.... :{

 

[dreamz25]

still undone.. :{

 

[Simon Bridge]

If you are really stuck you can always just go back to the calculus.