could you explain why we choose dm=p(2pir)dr? circular disk or cyllinder has a volume so shouldn`t dm be p(2pir)dr * thickness ? ( i attached an expression). Why we choose a dm of a ring (without volume)?
could you explain why we choose dm=p(2pir)dr? circular disk or cyllinder has a volume so shouldn`t dm be p(2pir)dr * thickness ? ( i attached an expression). Why we choose a dm of a ring (without volume)?
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could you explain why we choose dm=p(2pir)dr? circular disk or cyllinder has a volume so shouldn`t dm be p(2pir)dr * thickness ? ( i attached an expression). Why we choose a dm of a ring (without volume)?
Transcribed Image Text:fr
dm = p (2πr)dr x thickness
Transcribed Image Text:Circular Disc or Cylinder
To calculate the moment of inertia of a uniform circular disc of radius a and mass m, we
use polar coordinates. The element of mass, a thin ring of radius r and thickness dr, is
given by
(8.3.6)
dm = p2лr dr
where p is the mass per unit area. The moment of inertia about an axis through the center
of the disc normal to the plane faces (Figure 8.3.2) is obtained as follows:
I axis
The last step results from the relation m =
Equation 8.3.7 also applies to a uniform right-circular cylinder of radius a and mass
m, the axis being the central axis of the cylinder.
fr²p2лr dr = 2πp
4
ρπα?.
1
= {ma²
(8.3.7)
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but why we dont consider a thickness of mass dm ? ( of a disk)
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