# Moment of Inertia, Please, Today

• PremedBeauty
In summary, the conversation is discussing an experiment to determine the moment of inertia of a solid disk in two different ways: statically and dynamically. The calculated moment of inertia is smaller than the actual moment of inertia, with a percent difference of 3.6%. This could be due to errors in measurements or the assumption of a perfectly uniform disk. However, the rotational inertia should be the same in both cases.
PremedBeauty
Hello,

I have some questions:

1. Do you think the calculated moment of inertia is larger or smaller than the true moment of inertia? Explain.

for static moment of inertia I have:.0202kgm^2
for dynamic " ":.0195 kgm^2

In this case, it's smaller but I don't know why.

2. Is the percent difference in accord with your answer to #2? Give plausible explanations/causes to account for the difference. for the percent difference I got 3.6% which is small so it does agree with #2. I am not sure why there is a difference though.

3. The wheel could replace the pulley on Newton's law's 2nd law. Try to rethink an answer to the question: "If the pully has a fairly large mass, how will the result of this experiment be affected? "

You might want to state the full problem exactly as given so we can understand your questions.

I'm sorry, those are the questions my professor gave us.

the question:
2. Is the percent difference in accord with your answer to #2? Give plausible explanations/causes to account for the difference. for the percent difference I got 3.6% which is small so it does agree with #2. I am not sure why there is a difference though.

It's talking about question #1 on this board, not #2 (was question two on the paper).

PremedBeauty said:
1. Do you think the calculated moment of inertia is larger or smaller than the true moment of inertia? Explain.
Moment of inertia of what?

for static moment of inertia I have:.0202kgm^2
for dynamic " ":.0195 kgm^2
What do you mean by "static" moment of inertia?

You need to describe the problem you are trying to solve.

calculated moment of inertia in general.

You never hear of static or dynamic moment of inertia?

PremedBeauty said:
calculated moment of inertia in general.

You never hear of static or dynamic moment of inertia?
These concepts only make sense for an object that deforms when it rotates, like a speed governor. Since you seem to be unwilling to respond to Doc Al's request that you tell us what the problem is talking about, there is no way we can help you.

PremedBeauty said:
calculated moment of inertia in general.
What about it? Is calculated moment of inertia larger or smaller than the true moment of inertia? That would depend on how you're calculating it, wouldn't it?

You never hear of static or dynamic moment of inertia?
Not in the context of simple rigid body problems. Since a pulley is mentioned, I assume this is some kind of experiment with masses and pulleys. Why don't you describe the experiment?

Edit: OlderDan brought up deformable bodies; in such a case, static and dynamic moments of inertia will indeed be different. Are you talking about deformable bodies?

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experiment: In this lab you will determine the moment of inertia of a solid disk in two different ways and compare the results. It is somewhat like Newton's Second Law experiment where you determined the total mass of a system, statically by "weighing" it and then dynamically by measuring accelerations vs. force and taking the inverse of the slope of a line. There are differences, in that you will measure a single linear acceleration and the torque due to the tension in the tape will have to be considered. In addition, you will be required to "figure out" the expression to use in the determination of the "dynamic" moment of inertia. Refer to the sample problem done in class and there is another in the text, both of which contains the physics you need to know and all of the required equations. You just need to put the equations together in a different way suitable to calculate the moment of inertia using the dynamical results.

okay, my actual (which is the dynamic) is larger than the calculated moment of inertia (static). For actual, I got 0.0195, and the theoretical I got 0.0202. I was wondering the calculated moment of inertia is smaller than the actual. Does it have to do anything with the center mass of the wheel?

Also, when I did the percent difference (actual-theo/actual)X100 I got 3.6%. Does this account for the the calculated moment of inertia being small?

formula for static is I=1/2MR^(2)
formula for dynamic: I=R^(2)m(g-at)/at

It is confusing, I think this experiment was talking about deformed bodies, yes.

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PremedBeauty said:
okay, my actual (which is the dynamic) is larger than the calculated moment of inertia (static). For actual, I got 0.0195, and the theoretical I got 0.0202. I was wondering the calculated moment of inertia is smaller than the actual. Does it have to do anything with the center mass of the wheel?

Also, when I did the percent difference (actual-theo/actual)X100 I got 3.6%. Does this account for the the calculated moment of inertia being small?

formula for static is I=1/2MR^(2)
formula for dynamic: I=R^(2)m(g-at)/at

It is confusing, I think this experiment was talking about deformed bodies, yes.
So far, I see no reason to think that your experiment involved deformable bodies. What was the wheel made out of? How fast did it spin?

It looks like you are hanging a mass m from the wheel and letting it fall.

In this context, you are using "static" to mean: Calculated based on some model of the disk and measurements of R and M. How well did you measure those quantities? Was the disk perfectly uniform? (Unlikely, as it must have some axle to rotate.)

And you are using "dynamic" to mean: Calculated based on measurements of kinematic quantities like at (the acceleration of the falling mass), as well as m and R. Again, how carefully did you measure those quantities? What did you actually measure? Time to fall a given distance?

In both cases, the rotational inertia should be the same. Any differences are most likely due to errors in your model or measurements.

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## 1. What is Moment of Inertia?

Moment of Inertia, also known as rotational inertia, is a measure of an object's resistance to changes in its rotational motion. It is determined by the mass distribution of the object and the axis of rotation.

## 2. How is Moment of Inertia calculated?

Moment of Inertia is calculated by multiplying the mass of each particle in the object by the square of its distance from the axis of rotation and adding all of these values together. It is typically denoted by the symbol I and has units of kg*m^2.

## 3. What is the significance of Moment of Inertia?

Moment of Inertia is an important concept in rotational motion as it determines how much torque is needed to cause an object to rotate at a certain angular acceleration. It also plays a role in the stability and balance of objects.

## 4. How does Moment of Inertia differ from Mass?

Moment of Inertia measures an object's resistance to rotational motion, while mass measures its resistance to linear motion. They are related, but not the same, as an object's mass distribution affects its Moment of Inertia.

## 5. Can Moment of Inertia be changed?

Yes, Moment of Inertia can be changed by altering the mass distribution of an object or by changing the axis of rotation. For example, a figure skater can change their Moment of Inertia by pulling their arms in, thus reducing their mass distribution and allowing them to rotate faster.

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