Understanding this law makes it easier to learn about the various forms energy takes and how they relate to one another. The law of conservation of energy (which says that energy can change form but is never lost) ties together such topics as food calories, batteries, heat, light, and watch springs. For example, what do a bag of chips and a car battery have in common? Both contain energy that can be converted to other forms. It is the underlying order of nature that makes science in general, and physics in particular, so enjoyable to study. We have found that nature is remarkably cooperative-it exhibits the underlying order and simplicity we so value. As humans, we make generalizations and seek order. In the face of all these details, we have discovered that a surprisingly small and unified set of physical laws can explain what we observe. From the flight of birds to the colors of flowers, from lightning to gravity, from quarks to clusters of galaxies, from the flow of time to the mystery of the creation of the universe, we have asked questions and assembled huge arrays of facts. Over the centuries, the curiosity of the human race has led us collectively to explore and catalog a tremendous wealth of information. Every day, each of us observes a great variety of objects and phenomena. The physical universe is enormously complex in its detail. Because it's very hard to drawĪ 4, 5, or 20 dimensional arrow like this.Figure 1.2 The flight formations of migratory birds such as Canada geese are governed by the laws of physics. In four dimensions itīecomes more abstract. And as we study moreĪnd more linear algebra, we're going to start extending And you'll see because this isĪ 3, 4, 5 triangle, that this actually has a magnitude of 5. Pythagorean theorem to figure out the actual So this vector mightīe specified as 3, 4. Start at the end of the arrow and go to the front of it. Up and how much we're moving to the right when we Literally thinking about how much we're moving It's shifting three in the horizontal direction,Īnd it's shifting positive four in the vertical direction. You were to break it down, in the horizontal direction, The first coordinate represents how much we're moving You might also see notation, andĪctually in the linear algebra context, it's more This one only moves in the horizontal dimension. In each of these dimensions? So for example, Numbers that tell you how much is this vector moving If you're in two dimensions, to specify two Like you can really operate on that easily. It in your notebook, you would typically put a If you're publishing aīook, you can bold it. Represent a vector, is usually a lowercase letter. It with a little bit more mathematical notation? So we don't have to So for example, this wouldīe the exact same vector, or be equivalent vector to this. Not care where we start, where we place it when we thinkĪbout it visually like this. Now, what's interestingĪbout vectors is that we only care about the magnitude West, that would be north, and then that would be south. Horizontal axis is say east, or the positive horizontalĭirection is moving in the east, this would be So for example, I could startĪn arrow right over here. To the right, where we'll say the right is east. Our straight traditional two-dimensional vector We can mathematically deal with beyond three And then even four, five, six,Īs made dimensions as we want. Magnitude, 5 miles per hour, and the direction east. And now we wouldn'tĬall it speed anymore. Miles per are due east, this is a vector quantity. So for example,ĥ miles per hour due east. Vector, we would also have to specify the direction. This is considered toīe a scalar quantity. Here, which is often referred to as a speed, is not a It's only specifyingĭirection this thing is moving 5 miles per hour in. This information by itself is not a vector quantity. You that something is moving at 5 miles per hour, Of what wouldn't and what would be a vector.
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