Moment of Inertia Lab for discs of mass

[errorbars]

Homework Statement

We recently had a Physics lab where we were expected to find a relationship between the moment of inertia and discs of varying radius (discs have same mass), and develop a general equation to illustrate the relationship between moment of inertia and radius for discs of any mass.

Homework Equations

The general formula of the line is Inertia = (constant k)Radius^2 + Inertia_0
Inertia = mr^2((g/a)-1)

The Attempt at a Solution

I have managed to determine the average time, acceleration, and moment of inertia with the experimental time. I have figured out that the relationship between disc radius and moment of inertia is Inertia = Radius^2 (I believe). However, my current problem is a graph of Inertia vs Radius^2 -- my current line of best fit is y=0.7767020443x + 0.00017554163. The general formula of the line is Inertia = (constant k)Radius^2 + Inertia_0 . I have been unable to isolate k, and thus determine the relationship between k and the mass of the discs. (it should be a basic fraction). Also, I am having trouble understanding the significance of Inertia_0 -- should there not be any inertia if the disc has a radius of 0?

Thanks for any assistance you can offer!

 

[Delphi51]

Welcome to PF, errorBars!

So x is R², right? And you have y=0.7767020443x + 0.00017554163 which is really Inertia = 0.7767020443R² + 0.00017554163
compared to Inertia = kR² + Inertia_0
It looks pretty straightforward to identify the values of k and Inertia_0.

You would normally expect Inertia at radius zero to be zero since a disk with radius zero really doesn't exist, but in any experiment you probably have a shaft on the disk with some inertia. In view of your nickname, you must have error bars on the graph and an estimate of the accuracy of your slope and y-intercept. Is the 0.00017554163 larger than the error in it? If not, I think you would conclude that it is zero to within experimental error.

 

[errorbars]

Welcome to PF, errorBars!

So x is R², right? And you have y=0.7767020443x + 0.00017554163 which is really Inertia = 0.7767020443R² + 0.00017554163
compared to Inertia = kR² + Inertia_0
It looks pretty straightforward to identify the values of k and Inertia_0.

You would normally expect Inertia at radius zero to be zero since a disk with radius zero really doesn't exist, but in any experiment you probably have a shaft on the disk with some inertia. In view of your nickname, you must have error bars on the graph and an estimate of the accuracy of your slope and y-intercept. Is the 0.00017554163 larger than the error in it? If not, I think you would conclude that it is zero to within experimental error.

Thanks!

I just have a bad feeling about k though... shouldn't k be somewhere around 1/2 of the mass of the discs according to the equation for moment of inertia? (I=(1/2)mr^2)? Unfortunately 0.7767 is not half of 0.5 kg... hm...

Hm, that's what I suspected for the y-intercept. That's probably why the discussion asks how the friction in the axle bearing affects the results? :P

 

[Delphi51]

Yes, k should be half the mass. I have no idea why it isn't.
It might be worth going back to the original data and checking one or two or the runs individually to see whether the k is close to the .77. If so, look for some error in the calculations. Always worth eyeballing the graph and calculating the slope by hand! Calculators can get the wrong answer just as fast as the right one.

 

[rwisz]

I commend you for your efforts in conducting this lab and analyzing the data. From your results, it seems that you have successfully determined the relationship between disc radius and moment of inertia. However, as you mentioned, you are having trouble isolating the constant k and understanding the significance of Inertia_0.

To isolate k, you can rearrange the equation to solve for k: k = (Inertia - Inertia_0)/Radius^2. This will give you a value for k that you can then use to determine the relationship between k and the mass of the discs.

Inertia_0 represents the moment of inertia when the disc has a radius of 0. This value may seem insignificant, but it is important in determining the overall relationship between moment of inertia and disc radius. It can also serve as a baseline for comparison with the moment of inertia at other disc radii.

I would also recommend further analysis and experimentation to validate your results and ensure accuracy. Keep up the good work in your scientific endeavors!