Question

A compound disk of outside diameter 144 cm is made up of a uniform solid disk of radius 36.0 cm and area density 5.00 g/cm2 surrounded by a concentric ring of inner radius 36.0 cm , outer radius 72.0 cm , and area density 2.30 g/cm2 .

Find the moment of inertia of this object about an axis perpendicular to the plane of the object and passing through its center.

Answer 1

let R1 = 36 cm = 0.36 m

R2 = 72 cm = 0.72 m

mass of the disk, m1 = areal density*Area

= 5*pi*36^2

= 20357 grams

= 20.357 kg

mass of the ring, m2 = areal density*effective area

= 2.3*pi*(76^2 - 36^2)

= 32370 grams

= 32.37 kg

Moment of inertia of the object = moment of inertia of the disk + moment of inertia of the ring

= m1*R1^2/2 + m2*(R1^2 + R2^2)/2

= 20.357*0.36^2/2 + 32.37*(0.36^2 + 0.72^2)/2

= 11.8 kg.m^2 <<<<<<<<<<-------------------Answer