Question

The moment of inertia of a thin uniform circular
disc about one of the diameters is I. Its moment of
inertia about an axis perpendicular to the plane of
the disc and passing through its centre is:​

Answer 1

Answer:

Let mass of circular disc is M and radius R.

Given, Moment of Inertia (MOI) about one of its diameter=l, ⇒  

4

MR  

2

 

​  

=l  ⇒MR  

2

=4l   .....1

MOI about an axis passing through the centre of the disc=  

2

MR  

2

 

​  

 

Using parallel theorem of MOI, I=I  

cm

​  

+mx  

2

 , Where I  

cm

​  

 is MOI of centre of mass and x is the distance between centre of mass  and axis of rotation.  

MOI about an axis tangent to disc and perpendicular to its plane=  

2

MR  

2

 

​  

+MR  

2

=  

2

3

​  

MR  

2

=6l   (Using equation 1, MR  

2

=4l)

Explanation:

Answer 2

Answer:

Let M and R be the mass and radius of the disc respectively.

Moment of inertia about AB is I.

Moment of inertia about an axis passing through O and perpendicular to the plane, I

O

=

2

1

MR

2

Moment of inertia about an axis passing through C and perpendicular to the plane, I

C

=I

O

+MR

2

I

C

=3I

O

Using perpendicular axis theorem, ⟹I

O

=2I

Thus I

C

=6I