Moment of inertia rigid body problem

[haruspex]

0 for this rod, and the total would be 1/3mL^2 by itself?

We are not quite ready to go back to considering the rod. I am still asking about the point particle.

Edit: cancel that, see below.

 

[haruspex]

0 for this rod

Yes, the moment of inertia of a thin rod about itself as axis is 0.
Now use the parallel axis theorem to find its moment of inertia about the rod parallel to it in the H figure.

 

[i_hate_math]

Yes, the moment of inertia of a thin rod about itself as axis is 0.
Now use the parallel axis theorem to find its moment of inertia about the rod parallel to it in the H figure.

The parallel axis thrm states that I=Icom+mh^2
here it's I=0+mL^2=mL^2

 

[haruspex]

The parallel axis thrm states that I=Icom+mh^2
here it's I=0+mL^2=mL^2

Yes!
Do you see why this is? Every point of the rod is at distance L from the axis, so each little mass dm contributes L².dm to the total.

 

[i_hate_math]

Yes!
Do you see why this is? Every point of the rod is at distance L from the axis, so each little mass dm contributes L².dm to the total.

Yeah because its a rigid body of many particles. And adding them up, I-total=1/3mL^2+0+mL^2=4/3mL^2

 

[haruspex]

Yeah because its a rigid body of many particles. And adding them up, I-total=1/3mL^2+0+mL^2=4/3mL^2

In post #33 you came to understand that the moment of inertia of a rod about an axis parallel to it, distance L away, is mL². Why have you gone back to 1/3mL^2+mL^2?

 

[i_hate_math]

because I think the other rod that's perpendicular to the rotation axis also needs to be taken into account for the total MoI

 

[haruspex]

because I think the other rod that's perpendicular to the rotation axis also needs to be taken into account for the total MoI

Oh, ok, I didn't realize you were including that yet. In that case, yes, that is indeed the total MoI of the H shape about the given axis.

 

[i_hate_math]

Oh, ok, I didn't realize you were including that yet. In that case, yes, that is indeed the total MoI of the H shape about the given axis.

Thanks a lot mate for all the help and detailed explanations. I got the correct answer 6.45 eventually!