4 November 2014: Moment of Inertia Lab 16

Objective:
The purpose of this lab is to find the moment of inertia  of a disk. We must also find the deceleration of the disk due to friction. The validity of these two values will later be tested by making a prediction.
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There are three parts to this lab and so this blog will be divided accordingly

Part 1:
This part required that we find the moment of inertia of a spinning disk. This are pictures of the disk:

side view of disk

top view of disk

 As can be seen from the picture there are not just one object to calculate the moments of inertia but three: two small cylinders and one big disk.

The first thing to do was to gather the appropriate data needed to find moment of inertia. This included measurements and masses. The mass of the whole disk was given but the masses of the individual cylinders and disk were calculated. The measurements were gathered with the use of the caliper.







This is a picture of our calculated masses and the moment of inertia:

As you can see from the picture we round the radius of the disk was 0.0997 m and the height of it was 0.0155 m. The radius of the small cylinders was 0.0155 m and the length of each cylinder was 0.51 m. 

We then used these values to calculate the volume of each individual piece by the equation V= pi* (radius ^2)* height. We found the volume of the each small cylinder to 3.87 *10^-5. And the volume of the big cylinder was found to be 4.84*10^-4. Lastly we found the total volume to be 5.615*10^-4. 

With these volumes, we were able to calculate the masses of each individual piece by looking how much percentage of the total mass is made up of each individual piece. We knew that the whole apparatus 4.825 kg. We found that the percentage of the each small cylinder was 6.89% and thus the mass of each cylinder was 0.3324 kg. Lastly we found that percentage of the disk was 86.20% and thus the mass of the disk was 4.159 kg.

With these masses, we could find the moment of Inertia contributed by each individual piece. It was then found that each cylinder did not contribute to the moment of inertia. Therefore, the moment of inertia is just the moment of inertia of the disk which is defined by the equation I= mass*(radius^2). Therefore the moment of inertia of the disk was found to be 0.0207.

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Part 2:

This part of the experiment required that we find the angular deceleration of the disk as it slows down due to frictional torque acting on the apparatus. We did this by placing a piece of tape on the disk. We then set up a camera to record the disks' spinning, gave the disk a spin, and later analyzed the video.

We saved the video to our computer for further analysis and from the video, we were able to construct a graph. The data from the video gave us the tape's position and velocity in the x and y direction. Using the velocity in the x and y direction we were able to graph speed of the tape by the formula speed = sqr root((xvelocity^2) + (yvelocity^2)). Here are picture of the data tables and graphs:

As you can see by the linear fit we applied to our graph, the deceleration (a) is -0.04607. We then know that angular deceleration can be known by the equation: angular deceleration(alpha) = a/ radius. so then: 

our angular acceleration is -0.462 rad/(s^2).

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Part 3:

The last part of this experiment is to test the validity of our calculations. To do this, we connected this disk apparatus to a dynamics cart. This cart was to roll down an inclined track for a distance of one meter. But first we needed to calculate and predict how long the cart it should take for the cart to travel 1 meter from rest.

Here is a picture of the setup:

As you can see, a string attaches the cart to the disk apparatus, Also, the cart is on a track placed at some angle. The cart will be released at the top from rest.

Here is a picture of our calculations and prediction:

So as you can see from the calculations, our track was angled at 40 degrees. And we predicted our cart to take 8.27 s to travel on meter.

After this we actually let the cart go and timed the amount of time it took for it to go 1 meter. This was done using a stop watch. The time the cart took was 10 s.

We then used our predicted time and our actual time to find percent error:

So our percent error was 17.3 percent.

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Conclusion:

Our percent error was way too high to be valid. In truth we do not know exactly what went wrong. Our calculations are correct. We suspect that the problem lies our manner in getting angular deceleration and the way we analyzed the video. If our a is wrong then our alpha is wrong and thus this whole calculations are wrong. Although we do not know exactly what went wrong at least we know our math and approach is correct. This was an interesting lab as it showed us that calculations can predict real life events.