How Do You Calculate the Moment of Inertia for a Quarter Disc?

[Sumanth]

Find moment of inertia of a uniform quarter disc of radius R
and mass M about an axis through its centre of mass and
perpendicular to its plane ...

I tried in the following way:

I considered the relation. I= I_cm + Md²
Where d is the distance between required axis and centre of mass...
But i got wrong answer...

 

[SteamKing]

Find moment of inertia of a uniform quarter disc of radius R
and mass M about an axis through its centre of mass and
perpendicular to its plane ...

I tried in the following way:

I considered the relation. I= I_cm + Md²
Where d is the distance between required axis and centre of mass...
But i got wrong answer...

There's nothing wrong with your formula. However, it does require the use of the quantity (I_cm) you are asked to determine by the original problem.

Do you know the center of mass location for a quarter circle?

In this problem, you must not only determine in location of the c.o.m. (if it is not already known) and also the moment of inertia of a quarter circle. I think it will probably take a little calculus to do both.

 

[Sumanth]

K thanks for ur suggestion i will try to solve the problem

 

[haruspex]

There's nothing wrong with your formula. However, it does require the use of the quantity (I_cm) you are asked to determine by the original problem.

No, in this case i think the formula can be applied in the opposite direction usefully. It is relatively easy to find the M of I about the circle's centre (i.e. the corner of the quarter circle). Once the centre of mass has been determined, the M of I about that can be deduced from the formula.

 

[SteamKing]

It's not clear why the OP got the wrong answer as he posted no calculations. We don't know if he was using I about the origin, the c.o.m., or what.

In this case, Brevity is the enemy of Clarity, those two Irishmen who are eternal rivals.

 

[haruspex]

It's not clear why the OP got the wrong answer as he posted no calculations. We don't know if he was using I about the origin, the c.o.m., or what.

In this case, Brevity is the enemy of Clarity, those two Irishmen who are eternal rivals.

Sure, but I read your post as saying that the I_cm had to be found first before applying the formula. I'm just pointing out that in the present case it will be the other way about: the M of I can be found easily about a certain point that is not the centre of mass, then the formula can be used to find the I_cm.