Question

The moment of inertia of a disc about an axis
passing through its centre and perpendicular to
its plane is 20 kg m´2. Determine its moment of
inertia about an axis
coinciding with a tangent perpendicular to its
plane.
passing through a point midway between the
centre and a point on the circumference,
perpendicular to its plane.​

Answer 1

Answer:

Explanation:

Given,

Inertia at center is 20kg−m ^2

Let,

Mass of square plate, =m

Side of square, =a

inertia about perpendicular axis at center of square, I z=ma^2/6=20kg-m^2

​Apply perpendicular axis theorem

Iz= Ix+Iy=2Ix  (square has same side)

Ix=Iz/2=ma^2/12

Edge of square is at distance,a/2 from center

Apply parallel axis theorem, I(edge)=Ix+m(a/2)^2

=ma^2/12+m(a/2)^2

=ma^3/3=2×ma^2/6=2Iz

2×20=40kg−m^2

40kg−m^2