Moment of inertia (experiment)

[VVS2000]

So in the above image, I intend to find the moment of inertia of that black rotating object which rotates due to torque which is provided by placing mass on the pulley.
But the thing is that this rotating object is kind of like a ball bearing kind of system and even for a small torque it starts to rotate.
So is there any other things I can do with this experimental setup, like finding relationships among different physical quantities, or approximating the error on this ball bearing system, etc...
Any ideas please do post
Thanks in advance!

 

[BvU]

Hi,

Summary:: I encountered a problem while doing the experiment to find moment of inertia of a rotating object which has ball bearings

how did the problem manifest itself ? What have you done and found so far ?

So in the above image, I intend to find the moment of inertia of that black rotating object

You mean you did not find it yet ? What is your estimate ?

is there any other things I can do

Don't you want to solve your problem first ?

 

[sophiecentaur]

Don't you want to solve your problem first ?

Perhaps the OP though it was PF's job to do that.

 

[kuruman]

Summary:: I encountered a problem while doing the experiment to find moment of inertia of a rotating object which has ball bearings

So is there any other things I can do with this experimental setup, like finding relationships among different physical quantities, or approximating the error on this ball bearing system, etc...

What different physical quantities? What do you plan to measure? It seems to me you don't have a procedure for the experiment or if you do, you have not told us what it is.

 

[VVS2000]

What different physical quantities? What do you plan to measure? It seems to me you don't have a procedure for the experiment or if you do, you have not told us what it is.

No, I don't!
I am just doing experiments to figure things out which seems interesting

 

[VVS2000]

Hi,

how did the problem manifest itself ? What have you done and found so far ?
You mean you did not find it yet ? What is your estimate ?
Don't you want to solve your problem first ?

Ok so till now I have found the angular acceleration and from that I intend to find the Moment of inertia by equating it to mg×r
But it's here when I realized that my angular acceleration could be affected by this ball bearing system and my value might be less.
So yeah If possible please solve this first

 

[jbriggs444]

You still have not told us what you are controlling or what you are measuring. You have provided only a snapshot of your apparatus and not explained what it does or how it works.

You have "equated it [angular acceleration] to mgr". But since that is nonsensical, it is pretty obvious that you've actually done something else. What else is anyone's guess.

For some reason you are focusing on a "ball bearing system". It is not clear why.

 

[Lnewqban]

Can you post additional pictures showing that black rotating object in more detail and how it link to those bearings?
Could it be that the track over which that black rotating object rolls is not perfectly level and that gravity is making it move too easily?

 

[VVS2000]

You still have not told us what you are controlling or what you are measuring. You have provided only a snapshot of your apparatus and not explained what it does or how it works.

You have "equated it [angular acceleration] to mgr". But since that is nonsensical, it is pretty obvious that you've actually done something else. What else is anyone's guess.

For some reason you are focusing on a "ball bearing system". It is not clear why.

Ok let me explain clearly...
My aim is to find the moment of inertia of the black rotating object(kind of like a flywheel)
So as you can see in the previous apparatus pic, there's a string which goes from the spool of thread to this black rotating object and towards the pulley where we can suspend mass so as to rotate this black object
So we know that torque is equal to R×F.
F is given by mg, where m is the mass suspended by the pulley. And R is the radius of the rotating platform
Torque is also equal to I times angular acceleration, where I is the moment of inertia.
We can find angular acceleration by calculating the time period of rotation. And now, with all the requirements, I can go ahead and equate the two expressions for torque.
But the problem here is that since this is a ball bearing system, it tends to rotate "easily" even for small amount of torque.
So how can I get over this issue? Can I approximate the error of this ball bearings?
Or is there any flaw in my description? Pls let me know
Thanks

 

[vanhees71]

I'm not sure from what you write what the specific problem is though. What do you want to measure?

From your setup, I guess you let the mass on the pulley fall. Now all you need to measure is the acceleration of this mass. To see this let $\phi$ be the rotation angle of the rotating object, $a$ the radius of the spool and $z$ (with $\vec{e}_z$ pointing downwards, such that $\vec{g}=g \vec{e}_z$. Then the constraint reads $z=z_0+a \phi$. Let $\Theta$ be the moment of inertia of the spools, and you have
$$L=\frac{m}{2} \dot{z}^2 + \frac{\Theta}{2} \dot{\phi}^2 +m g z =\frac{1}{2} (m+\Theta/a^2) \dot{z}^2 + m g z,$$
and the equation of motion via the Euler-lagrange equation reads
$$\left (m+\frac{\Theta}{a^2} \right) \ddot{z}= m g \; \Rightarrow\; \ddot{z}=\frac{m a^2}{m a^2+\Theta} g=\text{const}.$$
Thus measuring $\ddot{z}$ and knowing $g$ at your place you can easily solve for the moment of inertia, $\Theta$.

Of course you should also discuss systematical errors (e.g., the above calculation entire neglected friction).

 

[gmax137]

are the bearings supporting the vertical shaft of the "object"? If so it seems to me they solve a problem, rather than creating one.

When you say "rotate easily" -- compared to what? Do you have an expectation of what should occur? Why are you surprised that small torques cause it to rotate?

 

[sophiecentaur]

@VVS2000 It would not be too difficult to measure the dimensions of your flywheel and also to have an idea what the material is (hence, the density). You can then use the MI formula in your lesson notes (or whatever). It isn't clear which are the massive bits but it looks as though you need to include both the two discs, the cylinder and the 'lumps' on the top of it; the MI will be the sum of the separate MIs. (Make up a table and add the four(?) contributions at the bottom.)

 

[vanhees71]

I thought you want to measure it. One way is my proposal in #10, if I understand your vague description of the setup right ;-).

 

[BvU]

Hello again, @VVS2000

I see a lot of reactions to the tune of "what is going on here" and I must agree that the two pictures do not constitute a useful description of the experimental setup.

• We see that the black contraption has moved between pic 1 and 2, so apparently is isn't bolted to the track.
• We see a spool with thread in pic 1 , which may or may not move with the black object on its own track ? In pic 2 the spool is replaced by a hand, which should severely ruin any chance of reproducible measurement.
• We see little cylinders
  
  on the disc that are not explained. Are they replacable weights to vary the moment of inertia ?

Please come up with a full description. If this is a lab exercise, also post the complete instructions.

And if a helper asks a question, answer it. We do want to help but you have to help us help you !

I will ask a mentor to move this thread to Intro phys homework.

 

[VVS2000]

Hello again, @VVS2000

I see a lot of reactions to the tune of "what is going on here" and I must agree that the two pictures do not constitute a useful description of the experimental setup.

• We see that the black contraption has moved between pic 1 and 2, so apparently is isn't bolted to the track.
• We see a spool with thread in pic 1 , which may or may not move with the black object on its own track ? In pic 2 the spool is replaced by a hand, which should severely ruin any chance of reproducible measurement.
• We see little cylinders View attachment 258442 on the disc that are not explained. Are they replacable weights to vary the moment of inertia ?

Please come up with a full description. If this is a lab exercise, also post the complete instructions.

And if a helper asks a question, answer it. We do want to help but you have to help us help you !

I will ask a mentor to move this thread to Intro phys homework.

I am really sorry for all the ambiguities.
As for those cylinders, yes you can remove them.
And no, this is'nt a lab exercise. I am just working with what is available in my physics lab.
The spool exists in both the pictures. There is no other person holding it.
Plz tell what and all confusions you have about this setup.
Thanks

 

[VVS2000]

I'm not sure from what you write what the specific problem is though. What do you want to measure?

From your setup, I guess you let the mass on the pulley fall. Now all you need to measure is the acceleration of this mass. To see this let $\phi$ be the rotation angle of the rotating object, $a$ the radius of the spool and $z$ (with $\vec{e}_z$ pointing downwards, such that $\vec{g}=g \vec{e}_z$. Then the constraint reads $z=z_0+a \phi$. Let $\Theta$ be the moment of inertia of the spools, and you have
$$L=\frac{m}{2} \dot{z}^2 + \frac{\Theta}{2} \dot{\phi}^2 +m g z =\frac{1}{2} (m+\Theta/a^2) \dot{z}^2 + m g z,$$
and the equation of motion via the Euler-lagrange equation reads
$$\left (m+\frac{\Theta}{a^2} \right) \ddot{z}= m g \; \Rightarrow\; \ddot{z}=\frac{m a^2}{m a^2+\Theta} g=\text{const}.$$
Thus measuring $\ddot{z}$ and knowing $g$ at your place you can easily solve for the moment of inertia, $\Theta$.

Of course you should also discuss systematical errors (e.g., the above calculation entire neglected friction).

No not quite. Why consider the radius of spool? Should't it be of the rotating platform?

 

[jbriggs444]

Ok let me explain clearly...
My aim is to find the moment of inertia of the black rotating object(kind of like a flywheel)
So as you can see in the previous apparatus pic, there's a string which goes from the spool of thread to this black rotating object and towards the pulley where we can suspend mass so as to rotate this black object
So we know that torque is equal to R×F.
F is given by mg, where m is the mass suspended by the pulley. And R is the radius of the rotating platform
Torque is also equal to I times angular acceleration, where I is the moment of inertia.
We can find angular acceleration by calculating the time period of rotation. And now, with all the requirements, I can go ahead and equate the two expressions for torque.
But the problem here is that since this is a ball bearing system, it tends to rotate "easily" even for small amount of torque.
So how can I get over this issue? Can I approximate the error of this ball bearings?

In a previous message in this thread I had asked: "What are you controlling" and "What are you measuring"?

It seems that what you are controlling is the mass of the object that is dangling from the pully.

It seems that what you are measuring is the time period of rotation. But how are you measuring this? Are you timing the period for one complete rotation starting from rest? For enough rotations to wind the weight down through a fixed distance? Taking a video and looking at position measurement for a known sample rate?

You write that torque is $R \times F$ where "R is the radius of the rotating platform". But that is not right. The $R$ that is relevant for torque is the radius of the spool around which the rope is wound. [It should be wound carefully in a helical pattern so that it does not overlay itself and thereby increase the effective radius].

You consider the ball bearings as if their lack of friction is a problem. *BOGGLE*. It would be a problem if they had a great deal of friction. A lack of friction is a good thing.

 

[VVS2000]

In a previous message in this thread I had asked: "What are you controlling" and "What are you measuring"?

It seems that what you are controlling is the mass of the object that is dangling from the pully.

It seems that what you are measuring is the time period of rotation. But how are you measuring this? Are you timing the period for one complete rotation starting from rest? For enough rotations to wind the weight down through a fixed distance? Taking a video and looking at position measurement for a known sample rate?

You write that torque is $R \times F$ where "R is the radius of the rotating platform". But that is not right. The $R$ that is relevant for torque is the radius of the spool around which the rope is wound. [It should be wound carefully in a helical pattern so that it does not overlay itself and thereby increase the effective radius].

You consider the ball bearings as if their lack of friction is a problem. *BOGGLE*. It would be a problem if they had a great deal of friction. A lack of friction is a good thing.

Yes you seem to have got almost everything right from the vague description I gave
Ok now I see I was wrong about the R. Thanks
And yes I am calculating for the time for enough rotations to wind the weight down and then the time period.
And as for the ball bearings, won't they affect the rotation speed because here we want the object to rotate without any such influences. By putting the ball bearings, it rotates faster than it should for even a small amount of torque.

 

[jbriggs444]

And as for the ball bearings, won't they affect the rotation speed because here we want the object to rotate without any such influences. By putting the ball bearings, it rotates faster than it should for even a small amount of torque.

Huh? Ball bearings reduce friction, but not to zero. They allow the wheel assembly to rotate faster than bronze bushings lubricated with cold molasses. But they do not make it rotate faster than, for instance, magnetic levitation might allow.

 

[vanhees71]

No not quite. Why consider the radius of spool? Should't it be of the rotating platform?

That's just geometry assuming that the thread unwinds from the spool. Then $z=z_0+a \phi$.

As I said, I had to guess the precise setup. You should provide simple drawings instead of photographs, which do not show the setup clearly.

 

[VVS2000]

That's just geometry assuming that the thread unwinds from the spool. Then $z=z_0+a \phi$.

As I said, I had to guess the precise setup. You should provide simple drawings instead of photographs, which do not show the setup clearly.

Ok I will try putting up a diagram

 

[VVS2000]

Huh? Ball bearings reduce friction, but not to zero. They allow the wheel assembly to rotate faster than bronze bushings lubricated with cold molasses. But they do not make it rotate faster than, for instance, magnetic levitation might allow.

So you're telling I will get a more accurate answer with the ball bearings?

 

[jbriggs444]

So you're telling I will get a more accurate answer with the ball bearings?

Ball bearings work better than bronze bushings with cold molasses, yes.

 

[VVS2000]

No but imagine if there were no ball bearings, won't the rotation then give the true moment of inertia?

 

[jbriggs444]

No but imagine if there were no ball bearings, won't the rotation then give the true moment of inertia?

If there are no ball bearings then you will have steel screeching on steel. Bearings are what we use to minimize friction when two bodies move against one another. Ball bearings do a good job at this.

The "true moment of inertia" has nothing to do with friction and everything to do with mass distribution.

 

[VVS2000]

If there are no ball bearings then you will have steel screeching on steel. Bearings are what we use to minimize friction when two bodies move against one another. Ball bearings do a good job at this.

True and the object will rotate on it's own. Which then gives the moment of inertia

 

[jbriggs444]

True and the object will rotate on it's own. Which then gives the moment of inertia

Both of those claims are false.
1. The object will not rotate on its own. [A rigid object will only commence rotation under the application of an external torque]

2. The resulting motion does not give the moment of inertia. [If you do not know the external torque, the resulting rotational acceleration does not allow you to compute the moment of inertia].

 

[VVS2000]

Both of those claims are false.
1. The object will not rotate on its own.
2. The resulting motion does not give the moment of inertia.

Own in the sense won't it rotate like there's something external other than the torque by the suspended mass is acting on it?

 

[jbriggs444]

Own in the sense won't it rotate like there's something external other than the torque by the suspended mass is acting on it?

What does Newton's first law say about objects that are subject to no external forces?

 

[kuruman]

No, I don't!
I am just doing experiments to figure things out which seems interesting

Let's go back to basics. You say you don't have a procedure yet you are "just doing experiments to figure things out". That is commendable but you need to have some idea of what you are trying to figure out so you can design and control your experiment in a way that will help you draw sensible conclusions. For example, Galileo wondered if heavier objects fall faster. So, he and an assistant dropped two balls of different weights from the tower of Pisa and saw which ball hit the ground first. That was their procedure motivated by the question "Which ball hits the ground first?" Humanity knew for centuries before Galileo that if you release an object it falls; that a heavy mass falling on you hurts more than a light mass falling from the same height; and that the higher the speed of a moving the more it hurts. What Galileo wanted to sort out was "does the heavier mass falling on you hurt more because it is moving faster or because of some other reason?"

The same applies here. Just observing your contraption do its thing without a question and a path to reaching the answer of that question will not buy you understanding.

 

[VVS2000]

What does Newton's first law say about objects that are subject to no external forces?

Sry I did'nt understand. Can you tell it in a diff way?

 

[VVS2000]

Let's go back to basics. You say you don't have a procedure yet you are "just doing experiments to figure things out". That is commendable but you need to have some idea of what you are trying to figure out so you can design and control your experiment in a way that will help you draw sensible conclusions. For example, Galileo wondered if heavier objects fall faster. So, he and an assistant dropped two balls of different weights from the tower of Pisa and saw which ball hit the ground first. That was their procedure motivated by the question "Which ball hits the ground first?" Humanity knew for centuries before Galileo that if you release an object it falls; that a heavy mass falling on you hurts more than a light mass falling from the same height; and that the higher the speed of a moving the more it hurts. What Galileo wanted to sort out was "does the heavier mass falling on you hurt more because it is moving faster or because of some other reason?"

The same applies here. Just observing your contraption do its thing without a question and a path to reaching the answer of that question will not buy you understanding.

Well yeah you're right. My aim is to try and find the moment of inertia of that object. But what I meant to say was I was'nt working on this experiment strictly based on a procedure. I did a similar experiment last semester and I just wanted to apply the same method or technique for this setup for finding the same thing

 

[kuruman]

Well yeah you're right. My aim is to try and find the moment of inertia of that object. But what I meant to say was I was'nt working on this experiment strictly based on a procedure. I did a similar experiment last semester and I just wanted to apply the same method or technique for this setup for finding the same thing

We can help you do that. What was the experiment you did and how did you do it?

 

[jbriggs444]

Sry I did'nt understand. Can you tell it in a diff way?

Newton's first law:
"An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force."

What does the above law say about the motion of an object that begins at rest and is subject to no forces?

It's not a trick question. It is a simple question intended to make you stop and think. But you have to actually answer it.

 

[vanhees71]

The following is equivalent to what I assumed above. It's for sure not a very accurate way to measure the moment of inertia, but in principle it's possible:

http://webpages.ursinus.edu/tcarroll/labmanual/node9.html

Much more accurate will be the measurement by using a torsion-pendulum setup like this:

https://www.mathworks.com/company/n...ving-mass-moment-of-inertia-measurements.html