# Moment of inertia: Answer without calculations

• Femme_physics
In summary, the problem asks for an estimate of the static moment of inertia of a planar shape, but apparently you cannot do this without calculations.
Femme_physics
Gold Member
To this shape

http://img10.imageshack.us/img10/2301/nocalculations.jpg

I'm asked to calculate the estimate of the static moment of inertia of the planar shape towards the x axis, that goes through its center of gravity. And then I'm told that I'm asked for an answer without calculations!

That's a bit taking aback doesn't it? How can I solve it without any calculations?

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I am not too sure if you can estimate it without doing any sort of calculation.

I think the keyword here is "estimate", meaning to do it with a minimum of calculations.

What you need to know is that moment of inertia is a summation of small areas times their distance squared.

For a rough estimate you can take the total area times the distance of the centroid.

So you would need to make an estimate of the total area.
Make an estimate of the distance of the centroid.
And calculate the area times distance squared.

But I'm told to "find the answer without calculations" -- literally. That contradicts you telling me to calculate!

The problem asks for a number. Afaik you can only get a number with calculations from other numbers.

So if you're not allowed to calculate at all, then I've got no clue either.

Btw, I just reread the problem, and it says: "the static moment of inertia of the planar shape towards the x axis, that goes through its center of gravity."

I do not understand which axis is meant here.

Let's agree it's a stupid, idiotic, pointless question then whose author needs to be slapped in the tush for it?

Hmm, there's is usually a point to questions, even though they might seem pointless at first.

Perhaps if you work it out with regular calculations, while keeping an eye out for a shortcut, you'll find something.
I really have no clue at this stage, but that's what I would do.
Even if there's nothing there, it's good practice.

I got some more important practices to do before the test, but thanks for your PoV!

As you wish. I'll see if I can make some sense of it this evening. ;)

I've thought about it some more and decided it is an idiotic problem.

I was thinking that perhaps you'd have to rearrange the shape around the axis in such a way that it would become a shape that you have listed.

But I don't see what shape that would be, and even calculating the centroid is a complex calculation with no simple answer.

I give up!

## What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is calculated by taking into account the mass and distribution of mass of an object.

## How is moment of inertia different from mass?

Moment of inertia and mass are related, but they measure different properties of an object. While mass is a measure of the amount of matter in an object, moment of inertia takes into account the distribution of that mass and how it affects the object's rotational motion.

## What factors affect moment of inertia?

The main factors that affect moment of inertia are the mass and distribution of mass of an object. Objects with a larger mass or a more spread out distribution of mass will have a higher moment of inertia and will be more resistant to changes in rotational motion.

## Why is moment of inertia important?

Moment of inertia is important in understanding an object's rotational motion and how it will respond to external forces. It is also crucial in designing objects such as vehicles, machines, and sports equipment where rotational motion is involved.

## Can moment of inertia be negative?

No, moment of inertia cannot be negative as it is a measure of an object's resistance to changes in its rotational motion. A negative value would not make physical sense.

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