# The objective for this experiment is find the moment

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The objective for this experiment is find the moment of inertia depends on axis for an object. Then prove the energy conservation for rotational motion. In this experiment, we use motion sensor to measure the angular position and time. Then we can get angular velocity and angular acceleration from computer. We hang a washer on the hook and twining rope with pulley’s track. Fix a rectangular object on rotary shaft to get static moment of inertia. Release the washer, make washer free fall, but let pulley and rectangular object do rotational motion. Repeat experiment with different pulley
and different axis for rectangular. We get the static moment of inertia with short axis for rectangular is 1.53*10 -4 and the dynamic moment of inertia for small pulley, medium pulley are 1.84*10 -4 and 1.64*10 -4 . For long axis, we get static moment of inertia is 9,39*10 -5 . Dynamic moment of inertia for small pulley and medium pulley are 1.17*10 -4 and 9.86*10 -5 . We can see there are some difference between static and dynamic moment of inertia. But the difference is not big. It means some error happened during experiment. When we calculate the energy for initial and final position, we get the difference in energy is only 0.0283, it means some energy lost in the motion, but overall energy are conserved. The possible error is friction exists between pulley and rope when pulley make rotational motion. It decrease the angular acceleration, thus dynamic moment of inertia is different from the static moment of inertia. Also, some energy conversion to heat and lost in the air. This can explain why energy lost in the motion. The error with measurement also cause the difference in result part. All in all, we find the dynamic moment of inertia is close to the static moment of inertia for same axis of rectangular object. We also prove energy conversed in rotational motion. Thus, I think we have achieve the objective for this experiment.