### Let's race some Soup Cans

#### Introduction

This project explores how the moment of intertia of different object will affect their acceleration while rolling down a ramp. We compare two cans of soup: A Chicken Broth and A Cream of Mushroom. These two soup cans have the same total mass and radius, but their contents are different. In the case of the broth, the soup is essentially water-like and won't rotate much as the can rolls down the ramp. The cream of mushroom however, is a gelatinous blob and will rotate with the can as it rolls. This creates different moments of inertia and should lead to different kinematics as the two cans roll down a ramp. We'll measure their positions using the Tracker motion software1 and analyze the results.

#### Moments of Inertia

The first step will be to characterize the two cans. Fig. 1 shows the two cans with a schematic describing the geometry of a soup can. It is a cylinder with a diameters of 0.065 m and a height of 0.100 m. The mass of the soup itself is 0.298 kg as indicated on the label. Placing the entire can on a scale shows that the mass of the soup plus the can is 0.341 kg, thus the mass of the metal can itself can be assumed to be the difference: 0.341 kg - 0.298 kg = 0.043 kg.

ComponentMass [kg]$R$ [m]$I$ (model)$I$Symbol
Broth0.2980.0325doesn't rotaten/an/a
Mushroom Soup0.2980.0325Solid Cylinder$\frac{1}{2}M_\rm{mush} R^2$$I_\rm{mush} Can walls0.02130.0325HoopM_\rm{wall} R^2$$I_\rm{wall}$

#### Conclusions

The results of the video analysis align fairly well with the predicted analytical results, though there are certainly some discrepancies. To improve the experimental set up, one could use better lighting, and perhaps frame the scene better in order to not have so much error in the velocity calculations. But, the main objective was met. We showed that the acceleration of the Cream of Mushroom soup as it rolled down the slope was close to the predicted value, and furthermore, was less than the acceleration of the Chicken Broth.

##### References
1. https://physlets.org/tracker/
2. Adapted from Hedberg, J.; Notes on Introductory Physics: https://hedberg.ccnysites.cuny.edu/PHYS207/SPRING-2021/notespdf/PHYS20700-torque.pdf