Angular Velocity Lab

 

Analysis

In this experiment, we analyze the energy conversion process of the system by comparing the experimentally measured velocity with the theoretically predicted velocity. In the experiment, we used the displacement 𝑥 and time t to estimate the terminal velocity of the falling object using the equation:

The theoretical predicted velocity is derived using an energy conservation model, calculated as:

where m is the mass of the suspended weight (0.1 kg), h is the drop height, r is the radius of the wire wrap, and I is the moment of inertia of the disk (estimated at 0.0014 kg-m²).

We performed a comparative analysis using three different radius values to calculate the predicted velocities for each case and compared them to the velocities measured in the experiments to assess the accuracy of the model and the sources of error.

Conclusion

By comparing the experimentally measured velocities with the theoretical predictions, we find that the predicted velocities are generally slightly higher than the experimental results, which is a reasonable phenomenon. The theoretical model ignores non-conservative forces such as friction, air resistance, and bearing losses, so the predicted values represent a maximum speed for an ideal case, which will be slightly lower than this in actual experiments due to energy losses. Of the three configurations with different winding radii, the case with the largest radius (𝑟 = 0.025) produced the highest linear velocity. The velocity increases as the winding radius increases, which is consistent with the energy model for 𝑟