Inertia is calculated by the equation 1 below. This equation relates to the plots of the two the results: lab and theoretical. Therefore, the gradients of these graphs give the value of inertia.
From the two tables and charts, the inertia can be computed. The computation is represented in the table below (the values of inertia are highlighted).
Mass
Lab Results
Theoretical Results
(kg)
Inertia (I)
Inertia (I)
0.1
0.9529
1250.67
0.000762
0.9523
1275.5
0.000747
0.2
1.8472
2553.33
0.000723
1.8838
1737.7
0.001084
0.3
2.706
3520
0.000769
2.7702
2560
0.001082
0.4
3.516
4535.33
0.000775
3.6228
3346.6
0.001083
0.5
4.295
5450.67
0.000788
4.443
4106.6
0.001082
Table 1: Comparison
From the table above, it is noticeable that inertia varies across depending on the mass of the object. Almost in the values, the theoretical values of inertia are higher than the lab results except at the mass of 0.1 kg. This exception can be due to the insignificant interferences of the environmental conditions on small masses. However, the general trend shows that the inertia values the theoretical computations are higher than those from the lab results.
Some of the factors that could have led to this difference include the fraction of the pulley, environmental conditions, and human error. One the side of human error it was possible to encounter inaccuracy when reading the angular acceleration values. The surrounding conditions exerted air resistance and the friction forces that could have interfered with the rate of angular velocity of the objects. The mechanics involved in pulleys may have also contributed to parameters such as acceleration of objects.
In conclusion, the theoretical total inertia values are higher than the lab values because of the possible sources of error encountered in the course of experimentation.
