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About this blog

As a Physics C student during the 2016-2017 school year at Irondequoit High School, I am interested in discovering how I can relate what I learn in the classroom to the world around me. This blog will include how I see physics in action in my everyday life.

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nathanstack15

As a saxophone player, I have always wondered how exactly sound waves work and why some notes sound good together while others don't. For example, when notes that are a half step apart are played simultaneously, "wobbles" are produced. If two sound waves interfere when they have frequencies that are not identical but very close, there is a resulting modulation in amplitude. When the waves interfere constructively, we say that there is a beat. The number of beats per second is known as the beat frequency, which is simply the absolute value of the difference in the frequencies of the two pitches. From a music theory standpoint, intervals can be referred to as consonances or dissonances. Consonances occur when tones of different frequencies are played simultaneously and sound pleasing together. Dissonances occur when tones of different frequencies are played simultaneously and sound displeasing together. According to a lecture by Professor Steven Errede from the University of Illinois, the Greek scholar Pythagoras studied consonance and dissonance using a device known as a monochord, a one stringed instrument with a movable bridge, which divides, "the string of length L into two segments, x and L–x. Thus, the two string segments can have any desired ratio, R = x/(L–x). When the monochord is played, both string segments vibrate simultaneously. Since the two segments of the string have a common tension, T, and the mass per unit length, mu = M/L is the same on both sides of the string, then the speed of propagation of waves on each of the two segments of the string is the same..." Basically, the ratio of the lengths of the two string segments is also the ratio of the two frequencies. Consonance occurs when the lengths of the string segments are in unique integer ratios. To learn more about the physics of consonances and dissonances, read his lecture here: https://courses.physics.illinois.edu/phys406/lecture_notes/p406pom_lecture_notes/p406pom_lect8.pdf.

nathanstack15

Recently in AP Chemistry, we talked about modern materials, like transistors, and how exactly they work. Transistors are a type of semiconductor. Semiconductors correspond with the metalloids on the periodic table. In Physics C, we typically refer to objects as either conducting or non-conducting, and have learned how to deal with electric fields, electric potential, electric potential energy, and capacitance for either of the two objects. The physics becomes more involved when considering semiconductors. Semiconductors have conductivities that are intermediate between conductors and insulators. The conductivity of a nonconductor can be increased by increasing its temperature because increasing the temperature increases the average kinetic energy of the nonconductor's electrons, making them able to be freed and flow to produce electrical current. One can also increase the conductivity of a semiconductor by chemical doping, which involves the presence of small amounts of other atoms. The following video explains how transistors work, and refers to n-type and p-type doping. 

 

nathanstack15

I recently saw this picture on one of my friend's Snapchat stories. How is this water bottle able to balance on its side? The bottle is positioned so that its net torque is equal to zero. On the left side of the bottle, the force of gravity due to all of the infinitesimally small pieces of its mass on one side of the system's center of mass multiplied by the distance that their weight vectors are from the center of mass (AKA the counter clockwise torque) has some definite magnitude. On the right side of the bottle, the forces of gravity due to all of the tiny pieces of mass multiplied by their distances from the center of mass equals a net clockwise torque on the bottle. The counter clockwise torque and clockwise torques applied to the bottle are equal in magnitude and opposite in direction, causing the bottle to remain in rotational equilibrium. The calculus behind this situation is quite complicated, as you can probably tell. 

Displaying IMG_1067.PNG

 

nathanstack15

This past weekend, I went to an IHS hockey game, and noticed that @SJamison was able to completely send his opponents off of their feet without even applying too great a force to the opponent. Skylor continually used the hip check, which seemed effortless compared to body checking and a lot less painful for the defender. What is the physics behind hip checking? By applying a force further from a player's center of gravity, a defender applies a torque to the other player, causing that player to experience a rotational acceleration which makes it easy for that player to lose his/her balance. The defender's hip does not need to apply a force other than letting the offender skate into their hip basically. By causing a rotational acceleration of any magnitude, an offender can easily lose their balance. Body checking is much more difficult, however, because in order to stop a player's momentum, the defender needs to have a momentum at least equal in magnitude and opposite in direction. 

nathanstack15

This past week in physics, we learned about Gauss's Law for electricity. It states that the electric flux, or the amount of electric field penetrating a surface, is proportional to the charge enclosed within the surface. Interestingly, Gauss's Law does not only apply to electricity: it also applies to gravity. According to Wikipedia, gravitational flux is a surface integral of the gravitational field over a closed surface. This is analogous to electric flux, equivalent to the surface integral of the electric field over a closed surface. Gauss's Law for gravity is mathematically represented by this equation:  \oiint{\displaystyle \scriptstyle \partial V}\scriptstyle \partial V {\displaystyle \mathbf {g} \cdot d\mathbf {A} =-4\pi GM}\mathbf {g} \cdot d\mathbf {A} =-4\pi GM , where \oiint represents a surface integral over a closed surface. Gauss's Law for electric fields states that:

\Phi_E = \frac{Q}{\varepsilon_0} = \oiint{\displaystyle \scriptstyle _{S}}{\displaystyle \scriptstyle _{S}} {\displaystyle \mathbf {E} \cdot \mathrm {d} \mathbf {A} }\mathbf{E} \cdot \mathrm{d}\mathbf{A} . Electric flux can also be represented by 4 pi k Q. Since G is the gravitational constant analogous to k for electricity, and since M is analogous to charge, it makes sense that total gravitational flux is equivalent to -4 pi GM. Gravitational flux is negative because gravitation fields always attract, where electric flux can be positive or negative depending on the enclosed charge.

nathanstack15

This past week in Physics C, we started the electricity and magnetism course. It has proven to be very difficult so far, especially when talking about electric fields and finding electric fields at a point by integrating across an object where its charge is uniformly distributed. I am even more scared to start learning about Gauss' Law. Since I do not entirely understand the hard stuff yet, I'll talk about simple electrostatics which can be seen in everyday circumstances. Charging by conduction, for example, occurs when materials become electrically charged by contact. This can be seen by rubbing a balloon against your hair. The atoms in your hair lose their valence electrons, which are transferred to the balloon, leaving your hair positively charged and the balloon negatively charged. If you place the charged balloon to the wall, it will stick because the wall is more positively charged than the balloon, and since opposite charges attract, the balloon sticks to the wall.

nathanstack15

Today was an unfortunate day in Physics class. After some bickering over some physics problem between my brother Jason and I, we decided that the only way to properly settle our dispute was to arm wrestle. Unfortunately, he beat me. Although I did not get the victory I deserved, I noticed that arm wrestling has quite a lot of physics to it. When arm wrestling, both people are trying to apply a greater torque than applied by the other person. Since torque equals the force applied times the distance from the point of rotation, the greater the arm length, the greater the applied torque. However, arm length plays a very small factor in terms of who has the advantage in an arm wrestle. According to Zidbits.com, "Stance, muscle density, stabilizer muscles, shoulder muscles, as well as where the specific tendons and muscle fibers attach to the bone are more important, and play a much larger role in arm wrestling. These same attributes are the reason why primates are generally much stronger than humans despite their smaller stature and size." In my opinion, Jason is not the true arm wrestling champion until he beats a primate. You've got a lot of work ahead of you @jcstack6

nathanstack15

This coming Friday, I'm going to Skyzone with a bunch of my friends. If you've never been to Skyzone, an indoor trampoline park, you definitely should go. I've been thinking about the ways that trampolines work, and notice that they demonstrate an important physical concept: conservation of mechanical energy. When jumping on a trampoline, your weight and work done by your legs causes the elastic surface of the trampoline to stretch and it causes the springs attached to the trampoline to stretch.  The springs and surface of the trampoline eventually stretch until the velocity of the person is 0 m/s. This is the point at which the springs and surface are at their amplitude. Since spring potential energy equals 1/2 k x^2, the greater the amplitude or maximum displacement from equilibrium, the greater the spring potential energy in the system. Since mechanical energy is conserved, the spring potential energy when the springs and surface of the trampoline are at their amplitude must equal the gravitational potential energy when the person jumping is at their maximum height. Therefore, the more work that your legs do in stretching the surface and springs of the trampolines, the greater their amplitude will be, causing the spring potential energy to be greater, causing the maximum height that you reach to be greater. 

Image result for sky zone trampoline park

nathanstack15

The other day, I was watching The Simpsons, one of my favorite TV shows, and noticed that in a particular scene, one of the characters, Mr. Burns, experienced multiple laws of physics in action. He was on a camping trip with his millionaire friends, and, with a shotgun, attempted to shoot a stationary pigeon. Mr Burns, who is unrealistically underweight, shot backwards dramatically after firing the gun. This occurrence demonstrates conservation of linear momentum. Originally, both him and the gun were stationary. After firing the gun, the bullet of relatively little mass travelled at an extremely high velocity in the positive direction. Since linear momentum is conserved, Mr. Burns' body was propelled in the negative direction at a high velocity because of how small the mass of his body is. Therefore, the mass of the bullet times its velocity minus the mass of Mr. Burns times his velocity is equal to 0. Mr Burns was, unfortunately, standing next to a lake, and was propelled into it. However, he did not sink in the lake. This occurred because of the surface tension of the water. The force of gravity on Mr burns is relatively small, considering how little he weighs. When he came in contact with the water, the surface tension of the water was greater than his weight, causing him not to accelerate into the water.

nathanstack15

Physics of Golf

One of my favorite sports to play is golf. I have played the game since I was about 8 years old, and have played on the golf team at school since 7th grade. I also play with friends over the summer pretty frequently. However, the game can be really frustrating due to the complexity of hitting a perfect golf shot. Hitting a golf ball well is much more complicated than simply keeping your eye on the ball and hitting it as hard as you can. Some people view a golf swing much like a baseball swing. However, they are very different. In a golf swing, there are two main components that result in the best possible shot. The first is having a good swing speed of the arms and shoulders. The second is letting the wrists rotate freely while still holding onto the club. On the downswing, when a golfer's hands are parallel to the ground, he/she must drop their wrists and allow them to move centripetally until after the ball has been hit. This maximizes the speed at which the club head strikes the ball because of the centripetal acceleration of the club. This is unlike a baseball swing, where the baseball player relies on strong forearms and wrists to exert a great force. The golfer's wrists, however, are passive in swinging through a golf ball. Also, by contacting the ball when the player's club is perpendicular to the ground provides the greatest acceleration of the ball because the applied force of the club of the ball is in the direction of the fairway, causing the ball to accelerate in that direction.

nathanstack15

This past weekend, I went ice skating for the first time in a couple years. I was not as good as I remembered, but I still had a lot of fun. When I was ice skating, a noticed a group of girls who looked like they were on a figure skating team. At one point, one of them went out on the ice. She did some fancy spins, like triple axles and stuff (I don't know very much about figure skating sorry), and I paid particular attention when she would spin. She began her spin with her arms and one of her legs out, and when she brought them in, her rotational velocity increased dramatically. This is a perfect example of the conservation of angular momentum. Angular momentum equals moment of inertia multiplied by angular velocity. When bringing her arms and legs in closer to her body, she decreased her moment of inertia by decreasing her radius (moment of inertia is proportional to mr^2 for any object). Since her initial angular momentum must equal her final angular momentum, the decrease in her moment of inertia causes an increase in her rotational velocity. Watch this cool figure skating video from the 2010 Vancouver Olympics to see for yourself.

https://www.youtube.com/watch?v=AbBe0MjtN1I

nathanstack15

Last week Rochester experienced a pretty heavy snow storm. Sadly, irondequoit was one of the only schools that didn't get a snow day. During the snow storm, I noticed a lot of snow plows hit the streets. Particularly, I noticed how the snow plows effectively get the snow off of the road. They have to angle their snow plows away from the center of the road in order to apply a force to the snow that has a component towards the sidewalks.  If instead they did not angle their plows, the snow would simply be pushed forward and not off of the streets because the force that the plow applies to the snow has no component towards the sidewalk. By exerting a force towards the sidewalk, the snow accelerates off of the road because of Newton's second law. 

nathanstack15

When I was younger, I liked to rake all of the many leaves in my yard into one big pile. Then, I would jump into the big pile along with my siblings. Why did I, like many young kids, love to jump into a big leaf pile? Let's consider the physics behind the scenario in terms of momentum and impulse. When in the air, the instant before I have come in contact with the leaves, I have a downward and rightward (assuming that I jump in the rightward direction) velocity, meaning that I have a non zero initial momentum. When my body hits the ground again, my velocity becomes 0. Therefore, my momentum has changed, meaning that I experienced an impulse. If the same jump is repeated, but the leaves are removed, my momentum changes by exactly the same amount as in the previous scenario, meaning that the impulse that I experienced was exactly the same, but I feel a greater force than I did in the previous scenario. That is because impulse is equivalent to the average force multiplied the time during which it is exerted. The leaves lengthen the amount of time during which the impulse is applied, meaning that the force that I experience is lesser when I jump into a pile of leaves. 

Image result for jumping into a big leaf pile

nathanstack15

Have you ever driven too fast over a speed bump and felt an uncomfortable jolt? Have you ever wondered why the feeling is so much less uncomfortable when you travel over the speed bump at a slower speed? This discomfort can be explained when considering the physics of speed bumps. When going over the speed bump, you experience an impulse, equivalent to the average force applied to you multiplied by the time during which it is applied. Let's say that you are approaching the speed bump at a relatively high speed, and that you roll over the speed bump in 0.001 seconds. The speed bump applies an impulse to you which stays constant no matter how fast you go over the speed bump. Since the impulse remains the same, the smaller the time interval during which you pass over the speed bump, the greater the force applied to you, which causes discomfort. Conversely, the greater the time interval during which you pass over the bump, the smaller the force you experience. When traveling at a slower velocity, you are passing over the speed bump for a longer time, making the force smaller. Therefore, speed bumps should be travelled over slowly in order to avoid a discomfortably large force. 

nathanstack15

When I was younger, I loved swinging on the playground swings. I always tried to go as high as possible because it made me go faster when at my lowest point, which was an exhilarating feeling. What I didn't understand then I understand now when considering the physics behind it. If you set your reference level at the lowest point of the swing, then when you first get on the swing, you have no mechanical energy. Then, when someone applies a force to you, they do work on you, causing you to accelerate and travel to a higher level. The work that they do in pushing you increases the mechanical energy of the system. The more work that they do to you, the more mechanical energy they add to the system. Since mechanical energy is conserved in a closed system, the potential energy at your highest point equals your kinetic energy at your lowest point. Therefore, the higher you are able to go, the more kinetic energy you will have at your lowest point, which means that you will travel at a higher velocity at the bottom of your swing. 

nathanstack15

Physics of Hot Rod

One of the most amazingly idiotic movies ever created is Hot Rod, starring Andy Samberg as stuntman Rod Kimble. In one scene, he attempts to jump a public swimming pool while on his moped. He fails miserably, as the video below illustrates. How could he have successfully jumped the pool? In order to determine this, lets consider the physics behind the situation. Lets say that the ramp is angled at 45 degrees to the horizontal. Lets also say the the the two ramps on the two sides of the pool are at equal heights. The width of the pool is approximately 15 meters. How fast would Rod need to be going while at the top of the ramp in order to clear the pool? We can use kinematics to solve this problem. Let v = the velocity at which he leaves the top of the ramp in order to clear the pool. The time for which he is in the air (t) equals the change in vertical velocity over the acceleration due to gravity [ t = (Vfinal-Vinitial)/g ]. Since the initial velocity in the vertical direction is Vsin45 and the final velocity in the vertical direction is -Vsin45, t can be solved for in terms of V. Therefore, t = (2^(1/2) / g) V . Now lets look at the horizontal plane. t = (2^(1/2) / g) V , acceleration in the x direction equals 0 m/s^2, and his displacement in the x direction equals 15 m. Since x= Vinitial t + 0.5at^2 and a = 0, x = Vinitial t . Since the horizontal component of V is Vcos45, we can solve for V by plugging in 15 meters for x , (2^(1/2) / g)V for t, and Vcos45 for Vinitial. Through this calculation, we find that Rod would need to be traveling at a speed no less than 12.12 m/s at the top of the ramp.

We can also think of the scenario in terms of energy in order to determine how much work his moped will have to do in order to reach this velocity at the top of the ramp. Lets say that the weight of his moped is 275 kg. Lets also assume that friction is negligible, meaning that mechanical energy is conserved in this situation. Where he begins at the top of the hill adjacent to the pool is about 2.0 meters higher than the top of the ramp (y = 2m). He travels about 10 m before reaching the top of the ramp. Also, his bike starts from rest. When he reaches the top of the ramp, all mechanical energy is in the form of kinetic energy. Therefore, an equation to model the conservation of mechanical energy in this scenario could be:

mgy + work done by the moped = 0.5mV^2

 

We can solve for the work done by the moped through algebraic rearrangement and by plugging in our known values: y = 2 meters and V = 12.12 m/s. Therefore, the work done by the moped is 14882.5 Joules. Since Rod travels a distance of approximately 10 meters before reaching the top of the ramp, and since Work = Fd, the force that his moped would need to apply for him to be able to clear the pool would be 1482.25 Newtons. He might need to buy a more powerful bike in order to be successful in doing this stunt. 
 

 

nathanstack15

One of my favorite things to do during the summer is water skiing. I don't go very often, but when I do, I love the satisfaction of getting up out of the water. In order to get up, you have to point your skis upward out of the water. By doing so, the skis are able to apply a force perpendicular to the direction of the velocity of the boat as the boat accelerates in the forward direction. This perpendicular force prevents the skier from face planting in the water. Then, you must tilt your skis to a lesser degree (as measured from the horizontal) in order to be pulled out of the water. By tilting your skis, the water applies a force, which has a component in the upward direction. This upward force pushes your skis upward until they are above the water level. The skis will remain afloat as long as the normal force to the skier, which is applied by the water, is equal to the downward force of gravity on the skier. Additionally, in order to avoid faceplanting in the water, the skier must recognize that as the boat accelerates in the forward direction, it will pull him/her forward. The skier then must apply an equal and opposite force to counter the force of the boat. water-skiing-5.gif

nathanstack15

One of my favorite sports to play is ping pong. I've always had a ping pong table in my basement and play with my brothers and with friends pretty frequently. I've always been amazed at the skill of Olympic table tennis players. If you've never seen Olympic table tennis, It's amazing how fast the little ball is hit back and forth between the two players. Sometimes it goes so fast that you can barely see it. The physics behind the game can explain why these Olympic athletes are so skilled at the game. In serving the ball, a player must throw the ball out of his hand at least 6 inches in the air and then hit the ball so that it bounces once on his/her side and once on his opponent's side. According to Newton's second law of motion, the greater the force that is applied to an object, the greater the object will accelerate. Olympic table tennis players hit the ball with great force, causing it to accelerate so rapidly that the ball can hardly be seen. Although they can serve the ball with such great force, their opponent is still able to return the ball without moving his paddle very much at all. The opponent does not need to worry very much about applying a great force to the ball as it comes towards him/her because of Newton's third law. An action force always has an equal and opposite reaction force. As the ball's inertia causes it to travel towards the opponent, it applies a force to the paddle, and the paddle applies an equal and opposite reaction force, causing the ball to accelerate in the opposite direction. Therefore, the force causing the ball to accelerate back towards the player who served it is caused mostly by the inertia of the ball. Watch this video below showing the best 10 table tennis rallies of all time. 

 

nathanstack15

I'm gonna be honest, I hate running. I love athletic games that require running, but I hate running just to exercise outside of the context of a sport. One of the most dreaded days of the IHS soccer season is the first day of double sessions. We have to run a mile and a half around the track in under 9 minutes and 20 seconds. It's a pretty difficult time to get, especially for those that don't do very much training beforehand. It requires a lot of mental toughness and determination. I can't begin to imagine the training that is required to break Olympic records in long distance running. High level athletes understand the difficulty in running long distance, and in order to better their performance, they consider the physics of running. The basic physics of running are pretty simple. A runner applies a force to the ground that is directed opposite the direction they are running. Then Newton's third law kicks in, and the ground applies and equal and opposite reaction force on the running, causing their body to be propelled upward and forward. In order to break records, runners must consider more than just the basic physics associate with their sport. According to Real World Physics Problems, in a 400m race  "the runner should accelerate as fast as possible for 1.78 seconds. This will enable him to reach a speed near his maximum. He should then maintain this speed for as long as he can. This speed will be such that 0.86 seconds before the end of the race his energy is entirely used up, and after this point is reached his running speed will begin to drop." Pretty crazy to think that runners consider how long to accelerate down to the millisecond. Watch this video to see the world record for the 400m, set by Wayde van Niekerk in Rio in 2016.

 

 

nathanstack15

One of the only games that I think I'll never get sick of playing is Spikeball. Spikeball is a new sport similar to both volleyball and foursquare. Two two person teams gather around a circular net. A point begins when a player serves a Spikeball by hitting the ball on the net so that it ricochets to the other team. The opposing team has three hits between them to hit the ball back on the net. If they do hit the ball back on the net, then the other team gains possession of the ball, meaning that they then have three hits between them to hit the ball back on the net. When a team does not hit the ball back on the net, the other team scores. Pretty cool, right? The game also involves physics, specifically Newton's laws of motion. In serving a ball, a player applies a force on the ball that causes the ball to accelerate and hit the net. The greater the applied force, the greater the ball will accelerate. Newton's third law of motion is demonstrated when the ball hits the net and ricochets off. Every action force has an equal and opposite reaction force - when the ball hits the net, the ball applies a force to the net, causing the net to react by applying an equal and opposite force on the ball. To get a better idea of how the game works, watch the tutorial video below.

 

nathanstack15

Shoot Your Grade Lab

This past Friday, our class attempted the "Shoot Your Grade" lab, in which we had to place a book on the floor where we expected a projected ball would hit. As a class, we all failed the lab because the book was not placed where the ball hit. The main reason for our failure was lack of communication between our class mates. Doing a lab with 25 people and having all those people working to solve the same problem can easily be chaotic and confusing, and it definitely was. If we had established agreed upon measurements, our final answers for where to place the book would have ideally agreed with each other (as long as people didn't make mistakes in calculation, or if they did make mistakes, they would have been able to identify where they were). Instead, we all calculated many different x velocities and ended up just picking one of them due to lack of time. The one we chose happened to be incorrect. 

 

In order to solve the problem, we needed to determine the initial velocity of the ball when shot by the launcher. In order to do that, we measured the angle at which the launcher was pointed, which was about 6 degrees above the horizontal. We then used a stop watch and took a slow motion video of the ball being shot to measure the time the ball was in the air. This was one calculation that varied between class mates; we all used different times in our calculations which gave us a wide range of horizontal velocities. Then, we measured the horizontal distance which we did agree upon. The horizontal velocity was calculated by doing horizontal distance divided by time. From there, we measured the height of the projectile from the floor and used that height, the acceleration due to gravity, and the time in order to find the vertical velocity. Here was where our calculations were incorrect. We calculated the vertical velocity incorrectly because we made the y displacement positive and the acceleration due to gravity negative, even though they were in the same direction. Therefore, vector direction was our biggest fault in determining the initial velocity.

 

I did the problem again using the same measurements but designating down as positive and up as negative and keeping the direction consistent. Then, I calculated that the initial velocity to be 4.68 m/s. When using this as the initial velocity and using -4 degrees from the horizontal as the angle for the second scenario, I calculated that the horizontal distance should have been 1.997 m. Images of my calculations are attached below.

calculations 2.JPG

calculations 1.JPG

nathanstack15

About Me

I am a senior at Irondequoit High School this year. I am particularly interested in Music, specifically playing the saxophone. I also enjoy playing sports, like soccer, basketball, golf, spikeball, tennis. I am a triplet, and have a total of 6 siblings, all of whom I am very close with. My strengths as a student are that I consistently work hard and complete things on time, and that math and science come naturally somewhat easy to me. I love working through math problems and being able to piece together what's given in order to create a meaningful solution. . I would like to attend Cornell University's College of Engineering next fall, with a major in Mechanical Engineering and a minor in Music. Two potential career goals of mine are that I would either like to work for Apple or I would like to work on making automobiles more environmentally efficient. 

I love problem solving, and I'm excited to do as much of that as possible while taking AP Physics C this year. I chose to take this course to better understand the world around and to understand physics as it relates to calculus. I hope to gain college credit for my AP scores in this class, to build new friendships, and to acquire a nearly complete understanding of the concepts taught in the course, and see how they relate to my interest in mechanical engineering. I am most excited about learning how calculus can be used to solve physics problems that I learned how to solve algebraically in Physics 1 and about completing labs to see the concepts that I learn are verified in the real world. I am anxious about E&M because the concepts of electromagnetism are difficult for me to visualize and understand. I am also anxious about the fact that my teacher does not lecture in class, that instead in order to learn I need to watch videos on Educator.com, which is something very new to me. I hope that I can understand the concepts well enough based on the videos. 

Overall, I'm excited about what I will learn this year!

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