Part 4: Analysis

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21 Part 4: Analysis

1. Transfer $R$ and $I_m$ to Table 3 of the Results section for Part 4.

2. Calculate the remaining values in Table 3. You can use the excel sheet to do this. Note that the Part 4 worksheet has already pulled your values for $R$ and $I_m$ from the Part 3 worksheet.

3. Plot a graph of $log(I_m)$ versus $log(R)$ on Lab 3’s Excel workbook under Part 4 worksheet. To make your plot:

a. Highlight the values under the $log(I_m)$ versus $log(R)$ column.

b. Then select the Insert tab and choose the Insert Scatter option under ‘Charts’. This will generate a graph from the two columns highlighted where the first column is the x-axis and the second column is the y-axis.

c. You can label the axes by clicking on your chart, selecting the “Chart Design” tab and then selecting the “Add Chart Element” option. This will allow you to customize many features of your plot.

d. **Important ** Make sure this graph is properly titled as it is a part of your grade. Also, properly scale your axes so that your data fits nicely within the chart area. To do this, right click on each axis, select ‘Format Axis’ and then play with the Minimum and Maximum bounds.

With your plot of $log(I_m)$ vs. $log(R)$ , insert a trend line in a similar manner to what was done in Lab 2. As a refresher, you can do this by:

1. Clicking on a data point on your graph. This should highlight all of your data points.

2. Right click, which will open a window, and select ‘Add Trendline.’

3. From the pop-up window, select ‘Linear’ as well as ‘Display Equation on Chart’ and ‘Display R-squared value’.

Copy your graph with the trend line and equation into the Part 4 Results section of your report.

Record the slope and y-intercept of the best-fit line drawn through the data points (you will need these values in your future analysis).

In this experiment you are not required to calculate uncertainties for the $I_m$ values or show uncertainty ranges on the graph.

Question 5.

For the $log(I_m)$ versus $log(R)$ plot, do the slope and y-intercept agree with the theoretical predictions of the moment of inertia of a point mass m situated at a distance $R$ from the axis of rotation? Explain why or why not using the values of the slope and the y-intercept.

Next, plot a graph of $I_m$ versus $R^2$ and determine the slope and intercept of the best-fit trendline through the data points. This is done in a similar manner to how the previous $log(I_m)$ versus $log(R)$ plot was made. Again, do not report uncertainties for these values on your graph or on your table. Make sure you report the trendline and the $R^2$ value on your graph.

Question 6.

For the $I_m$ versus $R^2$ plot, do the slope and intercept agree with the theoretical predictions? Explain why or why not using the values of the slope and the y-intercept, and provide possible causes of error if the values do not agree.

Question 7.

Based on your plot of $I_m$ versus $R^2$ , how well do our masses approximate point masses? Explain. Hint: The general theoretical expression for moment of inertia:

$I=\sum_{i} m_i R_i^2$ .

(Notice if all the masses $m_i$ are located at $R_i=0$ for all i, then I=0. However, there is a finite size to the masses $m_1$ and $m_2$ in your experiment…)

Question 8.

Explain why there may be any discrepancies between your results from the two plots you made. Describe any sources of error that may have arisen in the procedure for determining $I_0$ and $I$ .

Question 9.

What simple observation could be made from the experiment which would indicate that there is a loss of mechanical energy due to friction and air resistance?

21 Part 4: Analysis

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