Question

the M. I of an disc about an axis passing through its centre and perpendicular to its plane is 20kgmsqaure determine its M. I about an axis 1. coinciding with a tangent 2. passing through a point midway between centre and a point on the circumference perpendicular to its plane​

Answer 1

Answer:

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+ly=2lx (square has same side)

Ix=lz/2=ma^2/12

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

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

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

=ma^3/3=2xma^2/6=2lz

2x20=40kg-m^2

40kg-m^2

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