In this unit, we learned about standing waves and harmonics. Almost all the instruments are created according to these principles of waves in physics. One of those instruments is guitar. In this blog post, I'm going to explain the harmonics that are played by a guitar and the physics behind it. 

First, consider a guitar string vibrating at its natural frequency. Because the ends of the string are fixed in place, the ends of the string cannot move. Therefore, these ends become nodes. The most fundamental harmonic for a guitar string is the harmonic associated with a standing wave having only one antinode positioned between the two nodes on each end of the string. This would be the harmonic with the longest wavelength and the lowest frequency. The lowest frequency produced is known as the fundamental frequency/first harmonic of the guitar. Each of these frequencies or harmonics is associated with a standing wave pattern. The figures and the videos below depicts the standing wave patterns for the lowest four harmonics of a guitar string. 

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• The over all pattern of harmonics for a string instrument is: ​
  • ​with n being the number of harmonics, v being the wave speed, and L being the length of the string
    

When people see incredible movements in dance, they always say "it's physically impossible". However, as I dancer, I think that dancing is about defying the laws of physics while getting assisted by physics all the time. It was the laws of physics that make the movements possible, but it was also the laws of physics that make the movements difficult and challenging. People might be wondering how crazy can a dance be that is "physically impossible"? Here's a video of my favorite dancers on NBC World of Dance who do challenges the rules of physics in every single one of their dances. 

Now... In this blog post, I'm going to be discussing how aerials are related to all the topics I've learned in AP Physics 1 this year. 

To start off... What is an aerial? My answer is that it's just a cartwheel without your hands.
It took me 10 minutes to learn how to do an aerial when I first learned it, so obviously I did not think about the physics behind it, but now when I'm thinking about it, this one single motion has to do with many aspects in physics. So now... let's watch my tutorial on how to do an aerial!!!?‍♀️?‍♀️?‍♀️!!! how exciting lol

Now, how does each step relate to some physics concepts specifically? 
Step #1 - The Build-Up

• Kinematics - By running, I increased the speed that I'm moving in. There is an acceleration when I started to run. 
• Energy - The increase in speed directly results in an increase in kinetic energy (KE = 1/2mv^2)
• Momentum - The increase in speed also results in an increase in linear momentum since p=mv

Step #2 - The Hurdle

• Energy - During the hurdle, I transferred the kinetic energy I gained from running to gravitational potential energy since I jumped into the air. 
• Force - I exerted a force on the floor and the floor also exerts the same amount of force on me (Newton's 3rd Law Pair) to push me off the floor. 
• Kinematics + Force - On the way down back on the floor, my body is accelerating, which will result in an increase in Net Force since Net Force = mass * acceleration. This means that I'll be existing a greater force on the floor for the 3rd step. 

Step #3 - The Push-Off

• Force - this motion happens spontaneously but at the same time it is the most crucial step because this step determines the quality of the aerial. To the right is a great force diagram at the moment of the push-off. 

Step #4 - The Flip

• After tons of prep steps - now it is finally the "flip in the air" (Mr.Frost)! 
• Energy - the entire flip includes three main types of energy
  • Gravitational potential energy
  • Rotational Kinetic Energy
  • Linear Kinetic Energy
• Torque - the push-off exerts a torque on the system that includes me only, and that torque caused the following rotational motion of the body. 
• Inertia - I=mr^2, when I flip in the air, my arms are not wide open, I try my best to squeeze them in towards the center of mass of my body therefore to reduce the rotational Inertia and make the rotational motion to happen easier. 
• Projectile - When I'm in the air, the only force acting on my body is gravity, therefore, I'm an projectile when I'm in the air. 

Step #5 - The Landing

• From a dancer's perspective, bending your knees when landing is just a safety precaution
• However, from the physics perspective, bending the knees reduces the torque that would possibly act on the joints of the knees and therefore prevent oneself from injuries. 

Q&A
Why is it so hard to do an aerial in place without running? 

• This is mainly because without the build-up, there's no kinetic energy to build on to prepare for the flip, however, it is doable, you just need to push harder on the floor, so the floor can exert a greater toque on the body and make it flip. However, I have to mention that this is extremely hard to do. 

What are some ways to improve your aerials? 

• From a physics perspective, there are several ways to improve your aerials or make them prettier. 

1. Run Faster!!! ?‍♀️ Increasing the initial kinetic energy to begin with is always the most effective/easy way to get a great aerial. Since energy is conserved, the more energy you start with, the greater energy you will have when doing the actual flip
2. Pull in your ARMS!!! ? Reducing the Rotational Inertia by reducing the radius is not a hard thing to do, so this tip will work effectively too. 
3. Weight Loss???? The other way to reduce inertia is to reduce the mass of your body by losing some weight, but this will be less effective than pulling in the arms. According to the equation, if mass reduces by half, the rotational inertia will reduce by half as well, but if radius is reduced by half, the inertia will be 1/4 of the original inertia. It is obvious which way is easier to go for. 
4. Just gotta PUSH HARDER on the push-off!!!? The harder you push on the floor, the better the floor will assist you in getting up higher in the air. 

First of all, it is expected for the car to move in circular motion when it is making a right turn. With that being said, to make the we can assume that the linear velocity (v) and the mass (m) of the car are the same for both before and after the road construction. 
​Next, we can draw the diagrams. 

The equation of centripetal acceleration is on the right. 
From the equation, we can see that the centripetal acceleration is inversely proportional to the radius. In this particular problem, increase in the radius means decrease in centripetal acceleration. 
Since ∑F = Fc = m*centripetal acceleration (ac), we can conclude that the increase in radius will result in a decrease of  centripetal force of the car. 
In this problem, the centripetal force (Fc) is caused by friction (f). During the winter, when the road conditions may be icy and slippery, the friction on the road may not be big enough to hold the speeding turning car in its orbit. However, if we increase the radius, the the centripetal acceleration decreases and the centripetal force decreases as well, if we keep the linear velocity constant, less friction force is needed to keep the car on the track. 

Therefore, the road will be much safer after the construction, especially during the winter when the roads are icy with low friction. 

        IT WAS HARD but it was fine at the same time. It was a lot harder than I expected, and it was definitely challenging. The challenging part was when you don't have a number to calculate and you will have to work with variables. Variables made me very confused when I was taking the test. The multiple choice section was not very hard, but not easy either. Tests are never easy.
         I felt prepared for this test because I didn't have much problems when I was doing the Mastering-Physics assignment. But when I was taking the test I felt like I wasn't completely prepared. To study this test, I re-read the notes I took during classes, and I went through the power point we used. I also used the content page materials to study. I finished the packet Mr.Frost handed out the class before. The lab reports are very useful to study the graphs and the terms.
              I'm still alive after the test. I don't think I failed it, but I also don't think I did too well. I'm just glad that I got the test over with. I also talked to previous AP Physics 1 students and they said their high average scores have been around 85%, so I don't have a very high expectation on the score, meaning I take whatever score I get this time, but I will definitely be more prepared and hopefully do better next time. 

             On a scale of 1 to 10, I think I will give myself a 7/10 so far in AP Physics 1. I think this class is the right place for me because I can handle the work-load so far (plus I'm dropping Biology, so I'll get a free period to work). Also, I like the class a lot and I'm also having fun in class so far. According to your previous students😂, things are going to get crazy and intense throughout the year, and the fact that this class is of the hardest APs to score a 5 scares me a little bit, but I think I'm ready to take the challenge and make it through. I‘m actually worried about labs because I'm not very good at collecting data and just labs in general. In regard to the actual AP exam, I'm worried about not finishing the test because I usually solve problems very slowly, hopefully I'll be able to improve on this throughout the year. On the other hand, I'm excited for taking a science AP! I never thought that I was going to take an AP level science class in high school but I guess I am now. It is a challenge for me but challenges always make me better. BTW, I'm also excited for not having a final exam😏😏