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For my cylinder I used a can of Campbell chicken noodle soup.

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Using my measurements too much has caused a lot of confusion and annoyance in past, so I'm going to try to use them less in my calculations this portfolio.

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Of course I have to start with a free body diagram, like always!

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Calculation: Normal Force
Skill: Use ∑F = 0 and axes correctly

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Looks like we're digging into the rotational aspect of this scenario pretty quickly. I'm going to need to simplify this equation to find radial acceleration and static friction.
Skill: Use ∑F = mar and axes correctly

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Using the definition of Net Torque to simplify this equation.

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Using the definition of Net Torque to simplify this equation.

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We know that net torque is equal to the moment of inertia multiplied by angular acceleration. Since static friction is the only force that produces a torque about the center of mass of the cylinder, the torque is equal to the magnitude of static friction multiplied by the radius of the cylinder. I also know that the equation for the moment of inertia of a cylinder is I=1/2mr^2.
Skill: Use ∑torque = I⍺ correctly

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Now that I have a substitute for static friction that involves radial acceleration, I can insert it into the original equation to solve for radial acceleration.

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Calculating magnitude of static friction

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Calculating magnitude of static friction

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After calculating radial acceleration, I was able to use it to solve for the magnitude of static friction.

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I used the equation for the moment of inertia of a cylinder.

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Now that I know the radial acceleration along with the radius of the cylinder, I can easily find angular acceleration.

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Calculating Torque in two different ways

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Calculating Torque in two different ways

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Now that I know the static friction, moment of inertia, and the angular acceleration, I then calculated the torque in two different ways to double check the value. They turned out to be the same! That doesn't happen often for me.

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Since the cylinder starts at rest, there is no initial angular velocity, so I used the final angular velocity in this equation.

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Now it's time to use some rotational kinematics equations!
Skill: Use rotational kinematics equations
Okay, so this value is a long way off from my measured value of 1.05 seconds. I think it's because this calculated value doesn't take into account the distance that the cylinder actually travelled. None of these calculations actually used the displacement, so I can't be too surprised that the actual time elapsed was much longer than calculated.

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Now that I know the time elapsed, I can go ahead and calculate angular displacement.

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It's time to bring out the Big Ugly!

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In this scenario, work is equal to zero. Work is equal to F𝝙rcosΘ , and since normal force acts perpendicular to the incline, it equals zero since cosine of 90• is zero. Also, frictional force doesn't do any work in the scenario, since the cylinder is rolling. The frictional force is at the point of contact, but the force doesn't actually move, since the cylinder turns and there's a new contact point.
Skill: Use Big Ugly
Skill: Use Big Ugly with Rotational Kinetic Energy together in the same scenario

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Calculating measured Acceleration and measured Final Velocity

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Calculating measured Acceleration and measured Final Velocity

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I know I said earlier that I won't be using most of my measurements this scenario, but I wanted to see what the measured final velocity turned out to be, and compare it to the calculated final velocity. It actually turned out to be closer than I expected, because in past scenarios, my measured values were nearly always way off from my calculated values. 0.848 m/s and 0.750 m/s really isn't that big of a difference, all things considered. Either way, I'm going to use my calculated value for final velocity in future calculations.
Bonus Skill
Skill: Use Kinematics equations in a 1D situation

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***Calculating Final Velocity using Radial Acceleration

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***Calculating Final Velocity using Radial Acceleration

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Now, I'm not sure if this counts, but I wanted to try to calculate velocity using rotational kinematics, to fulfill the skill of Use Big Ugly and Forces/kinematics to solve for the same thing two different ways. This is rotational kinematics, and the values ended up being very different, so it has me thinking that this might not be worth any points, but hey, it was worth a shot!

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I absolutely love knocking out all these calculations right after one another, it's so satisfying!

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Ok, I'm going to admit right away, I had a lot of trouble with this scenario. I struggled to get it set up right, and went through so many water bottles trying to get a good trial, but I just couldn't really get it to work very well, and it was pretty impossible to get anything out of analyzing the video I took. It's only fitting that I struggled so much with this scenario, considering that the Fluids section was, for me, the hardest in the class by far. For some reason, I just couldn't get it to click in my head, which was clearly shown by my horrible grade last quiz. So, I just went ahead and calculated for whatever I could, which wasn't very much. I tried to make up for my lackluster attempt at this scenario by overachieving a little on the first scenario, so hopefully my portfolio still turns out okay as a final product.

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Calculating the Speed of Fluid for all 3 bottles 

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Calculating the Speed of Fluid for all 3 bottles 

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According to Bernoulli's Equation, the speed of water flowing out of the bottle is equal to the square root of 2gh, h being the height difference between the top of the water and the hole that the water is coming out of. This particular equation is specifically known as Torricelli's Theorem, which is a derivation of Bernoulli's Equation. The results of this calculation agree with what I saw while performing the scenario. The bottle with the hole drilled near the top clearly had the slowest stream, while the other two were too close to be discernible.
Skill: Use Bernoulli's Equation

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Experimentally Calculating Density of Water to compare to the theoretical density.

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Experimentally Calculating Density of Water to compare to the theoretical density.

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I figured a little extra physics couldn't hurt, so I conducted a little side experiment to see how well the density equation works. To find the mass of the water in the bottle, I poured it all into a cup, placed the empty bottle onto my kitchen scale, and pressed tare. Then, I poured all the water back into the bottle, and measured the mass to be 504 grams. (Now that I'm writing it out, I realized that I could have just skipped a step and tared the cup, but let's ignore that). Then, knowing that the volume of the water was 500 milliliters from the label on the bottle, I was able to calculate the density. It wasn't perfectly 1 gram per cubic millimeter, but 1.008 g/cm^3 is close enough!

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Cross Sectional Area of the Water bottle in two different ways

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Cross Sectional Area of the Water bottle in two different ways

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First, I used the equation for the cross sectional area of a cylinder, but I realize that a water bottle isn't a perfect cylinder, since it converges at the top into a drinking hole... or however you call it. So, in order to double check the validity of that calculation, I went ahead and tried calculating it a different way, using the volume I know and the height of the water that I measured. They turned out to be the same value!

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Calculating Force exerted by the Atmosphere on the inside of the bottle.

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Calculating Force exerted by the Atmosphere on the inside of the bottle.

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Now that I know the cross sectional area of the water bottle, and the fact that the bottle is open to the atmosphere (when the cap is off), I can calculate force. Only after I did this calculation, though, did I realize that this wasn't worth points. But it felt good to calculate, and it surprised me, because that's a lot of force!

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This portfolio was without a doubt the most challenging one yet, but it was rewarding!