Torque

Torque is the ability for something to turn on a certain axis. Torque is equal to lever arm times force. There is a center of gravity of every object and also an axis of rotation. The two are not the same but the torque of each object depends on both. The reason that this diver can flip so many times is because their center of gravity is in their waste and by pulling in both their arms and legs they make their axis of rotation where their center of gravity is as well. Their arms are legs are the level arms and because they are small the force is big therefore making the torque big.

Rotational Inertia and Angular Momentum

In this video you can see that the women is thrown up into the air at a small speed but gains tons of momentum when she is in the air by pulling her arms close together. This is has to do with angular momentum and rotational inertia. High rotational inertia means that most of the weight of an object is away from it's axis therefore making it hard for the object to turn. Low rotational inertia means most of the weight in near the center of the object making it easier to turn. This is when when she brings her arms in it adds weight to her axis therefore helping her turn more quickly, or lowering her rotational inertia. Angular momentum is when there are not many sharp angles on an object making it easier for it to turn or move quickly. This is also why when she draws her arms in she attempts to lay them as flat as possible on her chest, in order to have a lot of momentum by having not a lot of angles.

Unit Three Blog Reflection

In this unit we learned all about Newton's third law. Newton's third law states that every action has an equal and opposite reaction. For example, person pushes wall, wall pushes person. You are probably wondering how anyone ever moves anywhere if this is true. Well, take a horse and buggy for example. Horse pulls buggy, buggy pulls house. Buggy pushes ground down, ground pushes buggy up. This is the important part; horse pushes ground backwards, ground pushes horse forwards. That is why people walk and cars move and also why if you put a magnet in front of a magnetic car, it will not move because they will pull on each other and there is not another force causing them to move. Something that surprised me when learning this is we discovered that when an 18 wheeler and a small prius crash into each other, they both exert the same force because of Newtons third law. The only reason that a small car is more damaged is because it has a smaller force therefore a bigger acceleration, which connects to Newtons second law of acceleration equals net force divided by mass. Another thing we learned about is vectors, which relates to Newton's third law. When someone sleds down a mountain, where does their direction come from? Well, first of all, because of Newton's third law, sled pushes ground down, ground pushes sled up. This force up is equal to the weight of the sled/person, and is called the support force. Gravity, however causes a force to pull the sled directly downward, instead of diagonally downward to the mountain. If you take the support force line and the gravity line and make a square, you can connect the corners to find the actual velocity. This can be applied to which way a boat is going to go across a river with a current, pushing a couch with two people, and an object hanging in mid air connected with one string.

The next thing we learned about was the universal gravitational formula, which is a formula that can tell us lots of things but mostly it informs us about tides. The formula is force equals gravity (which equals around 7 times ten to the negative 11) times mass one multiplied by mass two all divided by the distance between the two squared. Though this sounds complicated, it is easy once you do it. The easiest way to think about this is when you relate it to tides. For example, when the moon is on the left side of the earth, the distance to the right side of the earth is very large, therefore the force on the ocean on that side of the earth is very small, since force and distance are inversely proportional in this equation. Obviously, this means that the tides on the right side of the earth are going to be low, because they have less force. This also means that the left side of the earth is a small distance away from the sun, meaning it will have a great force on it. This is why one side of the earth experiences high tides while the other experiences low tides. Now the moon is not always in the same place, so there are two different types of tides. When the moon is either above or below earth, the tides are called neap tides. These tides are higher or lower than normal tides because of the distance it is from the moon. The tides when the moon is on the right or left side of the earth are called spring tides. This is when there is a full or new moon, and the tides are average. Because the moon has a cycle of twenty seven days, the tides are different each day every month, therefore you can not predict them. 

The next thing we learned about after the universal gravitational formula and tides, was momentum and impulse. The formula for momentum is mass multiplied by velocity. We also learned about something called the conservation of momentum, which relates to another formula we learned about called the change in momentum. The formula for change in momentum is p(the symbol for momentum)final minus p initial. This is basically the same thing as the formula for conservation of momentum, however the conservation of momentum breaks down the change in momentum a little more. The conservation of momentum formula is mass one times velocity one plus mass two times velocity two equals mass one plus mass two times velocity one/two (which is the final velocity). Or, MaVa + MbVb = (Ma + Mb) Vab. This can be used to find any one of the variables in the equation, but it is mostly used to find the velocity after the collision. We learned about this through a lab where we took two carts and had them almost touching and then tapped a button which made them be pushes apart and comparing the momentum before to the momentum after. In the same lab we used those carts and had one moving one crash into a non moving one and found the differences in momentum. We learned that the conservation of momentum is directly related to newtons third law. We learned this through formulas. This is what we found:

Fa = -Fb (newtons third law, equal amount of force)

Fa∆t = -Fb∆t (acting for the same time)

Ja = -Jb  (impulse, which I'll explain in a second)

∆Pa= -∆Pb (conservation of momentum)

This is how one equals the other.

The last thing we learned about was impulse. The formula for impulse was j(the symbol for impulse) equals force times change in time. As you saw earlier, this can be related to momentum. The relationship between momentum and impulse is the reason why things like airbags and the mats on gym floors keep us safe. I will explain this through the mats on the gym floors example. The floors for gymnast are covered in pads because the gymnasts are going from moving to not moving. Which means they are going from having momentum to not having any momentum (referring to p=mv and ∆p=pfinal - pinitial). Because of this, the change in momentum wil always be the same no matter how long it takes them to stop. Change in momentum is equal to impulse (J = ∆p), therefore the impulse will also be the same. Because the impulse is force times change in time, the pads allow longer time to stop. The more time it takes to stop, the less force and therefore the less injury. In other words; 

J=f∆t

Or, if the mats were no there and it barely took any time to stop;

J=f∆t

What I have diffcult about all that we have studied is that it is hard to keep all the facts straight in my head. There are lots of formulas along with lots of confusing information that have to do with the same things, and they all originate from Newton’s third law. I have found it challenging to keep them all straight.

I overcame these difficulties, however, by relating each one to the different examples we learned in class. Once you relate it to an example in real life that we learned about in class, it is much easier to keep it all straight.

My effort in this unit has been up and down. Though I want to get a good grade, I often got frustrated with the difficult concepts that we were learning and at times I sort of gave up. However, the more close attention I paid to my homework and the harder I studied for quizzes the more that I found that I could do it and know exactly what was going on with a little big of hard work. My homework was pretty hard effort but my blog postings and class effort could have been stronger, which I have been trying to improve towards the end of the unit. I could have been a lot more persistent and creative, and my self-confidence was definitely not high. However, I thought my problem solving skills in this unit were particularly good, considering the past view have been very bad. I think my group members and I communicated very well however I could have had more patience in understand the problems.

My goal for the next unit is to always be persistent in believing that I will understand a topic no matter how difficult. I plan to do this by going in for extra help if I need it and always completing my homework with my full effort.

Besides the connections we made in class to everyday life, there are tons of things that this unit can be related to. An egg toss with conservation of momentum and impulse, car crashes, catching and throwing balls, and many other things. The main thing I think about when I think about this unit is throwing my phone from across the room. When I want to leave my dorm room and I need to put my phone down, I almost always throw it on my bed. I try to lean over to get as close as I can, and I pull my arm down so that the curve of my phone is higher. Now, I know why because of change in momentum, the universal distance formula, and impulse. 

Momentum and Impulse Picture

This is a picture of my friend Emily playing soccer. If Emily pulls this ball back with a force of 10m/s and the ball weighs 20kg, then the ball will have two hundred meters kilograms per second momentum because the formula for finding the momentum of an object is mass times velocity.

Impulse and Momentum of a Baseball

This video is a very quick summation of impulse and momentum. It talks about the equation for impulse, which is the force times the time, and it also tells us that impulse is equal to the change in momentum. The one thing that this video talked about that was different from what we learned in class is that the change is moment is equal to the mass times the change in velocity. In class we learned that the change in moment is equal to the final momentum times the initial momentum. Though these two things equal the same thing, it might be easier to stick to the one we learned in class. Other than that, this video is a really good short explanation and summary of impulse and momentum and how they relate to each other.

Tides Recourse

Unit Two Reflection

In unit two of physics, the first thing we learned about was newton's second law of motion. This law states that acceleration is directly proportional to force and inversely proportional to mass. This means that if the force increases, the acceleration will also increase. It also means that if mass decreases, the acceleration will increase. The lab that we did on this concept involved a cart, weights, and a hanging weight. We moved the weights around from the hanging weight to the cart and measured the acceleration on each change. In the lab, we constantly kept one thing concept. For example, we kept the force (or the weight on the hanging weight) constant and changed the mass of the whole system. Or, we kept the mass the same and changed the weight of the force (or the hanging weight). Through this, we found that acceleration is in fact directly proportional to force, meaning when one increases so does the other, and that mass is inversely proportional to acceleration. Meaning when one decreases, so does the other.

The next thing we learned about in physics was objects in free fall. In free fall, objects do not have air resistance and therefore only have the force of gravity act on it. The force of gravity is known to be 9.8 m/s squared. The two equations used when talking about free fall is velocity equals gravity times time and distance equals 1/2 gravity times time squared. We learned that acceleration is free fall is constant, meaning each second and object is gaining a speed of 9.8m/s^2. We also learned that in free fall, a penny and a feather will hit the ground at the same time because the only force acting on them is gravity. The lab that we did to demonstrate free fall was we used a steal ball to measure the height of third anderson. We did this by dropping the ball from the third floor, the top one, and recording the time it took for the ball to fall from the top of the floor to hit the ground. Using the average of a few different trails, we plugged this into the d=1/2gt^2 formula and found that our estimated height of third anderson was about 9 meters. Then, we took string and found that the actual distance was a little bit under 11, pretty close. 

The next thing we learned about was something similar to free fall but much more complicated. It's called projectile motion. Projectile motion is the affects on an object that does have air resistance and factors in the horizontal motion of an object. To get the horizontal velocity of an object you use the formula v=d/t. Of course, this can be rearranged to find the horizontal distance or how long an object traveled horizontally. Something that is different between vertical and horizontal velocity is that horizontal velocity stays constant throughout the time something is traveling through the air. However, vertical velocity gains 9.8m/s^2 each second when falling downward and looses 9.8m/s^2 when going upward. Projectile motion is used a lot when talking about skydiving. This is because when you are skydiving you are not free falling because you are greatly affected by air resistance. Once a person jumps out of a plane, they gain velocity as they fall until they reach something called terminal velocity. In terminal velocity, the weight of the object is equal to the air resistance on the object, causing the velocity to stay constant until something changes. This means that as the velocity increases, before terminal velocity, the acceleration is decreasing and is at 0 when the object is in terminal velocity. Once a parachutist reaches terminal velocity they can only stay there for a few seconds because they need to deploy their parachute on time in order to not get hurt when they hit the ground. The parachute helps the parachutist slow down, as we learned, because the two things that affect air resistance are surface area and speed. This means that the parachute adds surface area which also adds air resistance, causing the parachutist to slow down until the air resistance yet again equals its weight. However, this new terminal velocity is a lot slower than the original one due to the surface area of the parachute. Also, during this change the acceleration is not just decreasing but it is decelerating into the negatives. Projectile motion is not only used with parachutist, it can also be used with throwing things upward like shooting a cannon, throwing things downward like kicking a ball over a cliff, and dropping things out of air planes. The biggest example besides parachuting that we learned about was the difference between a falling piece of regular paper and crumpled up paper. Though it may seem like crumpling up paper could change its weight, causing it to fall faster, both of these things are incorrect. The reason that a crumpled up piece of paper falls faster than a regular piece of paper is simply due to surface area. Because the normal piece of paper has a bigger surface area, it is going to need more air resistance and therefore is going to take longer to reach a terminal velocity than a crumpled up piece of paper. 

What I have found difficult in what I have studied is separating each formula with each concept and not confusing the affects of gravity on an object in free fall compared to projectile motion. I overcame these difficulties, however, by really paying attention to each example and what they taught about the topic and how I could differentiate each concept by pairing them with their examples in my mind. 

My effort this unit, in my opinion, was even more than last unit. With the many different very difficult concepts we were learning I had to study even harder and make sure that I understood everything outside of class. Though this doesn't reflect in my grade, I felt pretty confident with the concepts because I understood a lot of the things we did in class. I thought that I problem solved pretty well in the labs and that I could express the concepts in both my spoken and written words. I tried to be patient with the work although at times it was difficult when the concepts became difficult, but altogether I thought that it was a strong unit regarding my work effort. 

My goal for the next unit, again, is to study more by completing every assignment on time even if I'm not 100% sure its right because I know now that learning from your mistakes is one of the best ways to learn.

Connections from this lab to everyday life are obvious; parachuting, things falling out of air planes, falling pieces of paper, exedra. But one thing that I noticed in everyday life that applied to physics that caught my eye was a balloon floating up to the sky. Though I'd seen it many times before, I had never though of the physics behind it.