Find out the moment of inertia of an annular area, Mechanical Engineering

Find out the moment of inertia of an annular area:

Find out the M. I. of an annular area among two circles where difference of radius is quite small, around any centroidal axis.

Solution

The centroid G of such a thin circular strip of small thickness t is at its geometrical centre as illustrated in Figure

Figure 4.36

We have, dA = ds × t

where  ds = Arc length = a × d θ

Letting the plane of the area in XOY plane (O and G coincide),

430_Find out the moment of inertia of an annular area.png

= 2 π a3 × t

= 2 π at × a 2

= (Area of annular strip) × a 2

=  A′ a 2

As the annular strip of area A′ is also axis symmetric, then I x  = I y ,

Hence, we have I x  =  I y  =    I z   /2 = A′ a2/2

Posted Date: 1/29/2013 1:28:12 AM | Location : United States







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