Results: Data Table: Circular Motion Length of Radius of Period of sin 0 String, L Orbit, R Revolution, T (cm) (cm) (s) R ( o) 20 18 0.5 40 35 0 .7 60 54 0. 8 80 69 0 9 100 90 1. 1 Graphs: Attach your two graphs to the back of this report. Analysis and Concluding Questions: 1. Calculate the average value of angle 0 found from using the formula sin 0 = R/L. 2. Compare your calculated value with the value of 0 predicted using cos 0 = m/M. What is the percent difference between the two results? 3. According to the results, what is the mathematical relationship between the period, T, of the orbiting mass and the length, L? 4. Determine the slope of your final, straight-line graph, and express it in the appropriate units.5. Write the specific equation for your straight line, incorporating the slope (make sure to include units). You can use the results of your experiment to do a check on the formula for centripetal force. Since therefore, T2 _ man2R 72 Fc Figure 2 shows that R = L sin 0 , and Figure 3 makes it clear that Fc = FTx = Mg sin 0. Therefore, we can write: T2 _ man Lsin e Mg sin 0 Mg Thus, the theoretical slope of a graph of T2 vs. L should be - man2 Mg 6. What is the theoretical value of your slope? 7. What is the percent difference between your graph's actual slope and the theoretical slope? Discuss sources of error in this experiment and how you might be able to reduce their effects