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

AI Thread Summary
To calculate the moment of inertia for a uniform quarter disc of radius R and mass M about an axis through its center of mass, the correct approach involves determining both the center of mass location and the moment of inertia of a quarter circle. The formula I = Icm + Md² is applicable, but it requires knowing Icm, which is the value being sought. The discussion highlights that while the formula is valid, the original poster may have misapplied it without proper calculations or clarity on the axis used. It is suggested that finding the moment of inertia about a different point first could simplify the process. Understanding these concepts is crucial for accurately solving the problem.
Sumanth
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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= Icm + Md2
Where d is the distance between required axis and centre of mass...
But i got wrong answer...
 
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Sumanth said:
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= Icm + 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 (Icm) 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.
 
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K thanks for ur suggestion i will try to solve the problem
 
SteamKing said:
There's nothing wrong with your formula. However, it does require the use of the quantity (Icm) 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.
 
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.
 
SteamKing said:
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 Icm 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 Icm.
 

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