Question

A compound disk of outside diameter 128 cm is made up of a uniform solid disk of radius 36.0 cm and area density 3.60 g/cm^2 surrounded by a concentric ring of inner radius 36.0 cm, outer radius 64.0 cm and area density 2.20 g/cm^2 Find the moment of inertia of this object about an axis perpendicular to the plane of the object and passing through its center. I =

Answer 1

momento of inertia of solid disk is

I = 1/2 md rd^2

for ring

Ir = 1/2 m r( r1 + r1)^2

I = Id + Ir

md = 3.6 g/ cm^2 ( pi ( 128/2)^2 = 38.58kg

I d = 1/2 ( 38.58) ( 0.64)^2 = 7.90 kg m^2

Ir = ( 2.2) pi ( 64^2 - 36^2 )

=19.34 kg

Ir = 1/2( 19.34) ( 0.64^2 + ( 0.36^2) )

=5.21

I total = 7.9+5.21 = 13.11 kg m^2