Question

what is the moment of inertia of a rod through an axis parallel to the axis passing through the centre of mass perpendicular to it?

Answer 1

Answer:

For the rod of mass M and length l,

I=Ml

2

/12. Using the parallel axes theorem, I

′

=I+Ma

2

with a=l/2 we get,

I

′

=M

12

l

2

+M(

2

l

)

2

=

3

Ml

2

We can check this independently since I is half the moment of inertia of a rod of mass 2M and length 2l about its midpoint,

I

′

=2M.

12

4l

2

×

2

1

=

3

Ml

2