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11. Repeat this twice more, obtaining four sets of readings altogether of times and heights. TABLE 1 a (mm) bo (mm) Ayo (mm) -3 mm 33 mm 37 mm Length of track 560 mm TABLE 2 Inclination of rails Rolling times Larger disc Smaller disc Height H (N-b Ay Log H Lower end Higher end aN (mm) b (mm) ts toveroge (mm) tveroge Log t Log t t 12.81 19.16 73 66 1 12.48 19.06 12.04 7.91 113 92 11.75 7.62 6.12 9.40 3 153 119 6.09 5.19 4.93 9.29 7.51 7.48 146 4193 CALCULATIONs AND RESULTS PROCESSING Use the Excel software or plot manually graph (log t) vs (log H) for the large and small disc on the same axis 1 Draw the lines of the best fit Find y-intercept for each line (c) Calculate k as antilog of 2c (k 10) 3. 4. 5. Show calculations of the moment of inertia for each disc using expression (7) 6. Record the result in the Table 3. Mass 3.253 Large Disc C K I.. Mass 1.363 Small Disc: C K . TABLE 3 Line of the best fit Moment of Inertia (kg mm2) y mxe C Large Disc Small Disc QUESTIONS AND OBSERVATIONS Question 1. Calculate theoretical values for the moment of inertia of the discs. Consider the rolling object as a solid disc plus a solid cylinder (protruding shaft) rotating around the same axis through their centres (Figure 2). Use the following data: Large disc Diameter 150 mm Small disc: Diameter 100 mm Mass of the shaft 0.127 kg Diameter of the shaft 12.5 mm Moment of inertia of a solid disc or cylinder: IMR /2 Figure 2 Moment of inertia of two objects rotating together around the same fixed axis can be calculated as sum of moments of inertia of each object. Theoretical moments of inertia: Large disc plus shaft Small disc plus shaft Question 2. Compare experimental and theoretical values of the moments of inertia. Discuss possible reasons for any discrepancies.

Answer 1

TABLE 1 b. Cmm) ao Cmm) Ary. (mm) 33 mm 37 -3 length of thack = 560 mm TABLE 2 1mclination Rolling times hails Smaller disc Height larger disc Higher end Lower end aN CMm) bN Cmm) H boT (Ma t2 kawgLogt tavg Log t t (mm) /9.11 12la 8 12.48 9.16 ta 64 10 73 66 a1 19.06 7.9 2.04 776089 -08 11-89 I13 92 11.75 T.62 9-40 6-12 G10 0-78 9.34 0.97 153 119 -a38 2 6 09 9-29 5 19 7-51 506 070 +.49 0.87 - 3 29 4 14-6 193 4.43 7.48 po ble to compute Ayo 8hould be posthine Not