Rotational Kinematics lab

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1. Use the velocity components to determine the direction of the velocity vector. Is it in the expected direction? 1. From the x-t and y-t images, the two curves show a sine and cosine relationship, indicating that the object is in uniform circular motion. Since position over time behaves as a sine and cosine function, this means that the velocity is their derivative, and the direction of the velocity is always perpendicular to the direction of the radius, so the velocity vector varies in the tangential direction, which is consistent with the theory of circular motion. The formula used to calculate speed 2. Analyze enough different points in the same video to make a graph of the speed of a point as a function of distance from the axis of rotation. What quantity does the slope of this graph represent? In this experiment, we investigated the relationship between radius, linear velocity and acceleration in uniform circular motion by analyzing the motion of three different points on a r...
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Frictional Force

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Data collected from the experiment

The formula to calculate the normal force and friction force is

Predicted Friction Force

Mass change graphs and tables

tables
graphs

In the graph above, the orange line represents the predicted relationship fk=μkNf_k = \mu_k N, using a theoretical coefficient of kinetic friction μk=0.4\mu_k = 0.4. The experimental data yields a fitted slope of approximately 0.8911, indicating that the actual friction observed in our experiment was significantly higher than the expected value.

Hight change graphs and tables

tables

graphs

In the height-changing trial, the measured coefficient of kinetic friction was μₖ ≈ 0.315, with a high linearity of R² = 0.9574. This closely matches the predicted value of μₖ = 0.4, supporting the direct proportionality between kinetic friction and normal force.

Uncertainty


To evaluate the uncertainty in our experimental method, we conducted four repeated trials at the same setup. The standard deviation of the measured time was ±0.12 s, resulting in a friction force uncertainty of ±0.01 N. The normal force remained constant. These values indicate a reasonable level of precision, although small timing errors still contributed to the variability observed in the mass-changing trials.

Conclusion

The measured coefficient of kinetic friction for wood on aluminum was found to be μₖ ≈ 0.89 in the mass-changing trial, and μₖ ≈ 0.32 in the height-changing trial. These values show significant variation, likely due to timing uncertainty and different experimental conditions. Compared to the predicted value of μₖ = 0.4, the height-changing result closely matches the expectation, while the mass-changing trial overestimated μₖ, possibly due to greater experimental error (as indicated by a lower R² value). Overall, the data supports the theoretical model fk=μkNf_k = \mu_k N, but highlights the importance of controlling measurement uncertainty.





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