So let's have a quiz.In physics, a force is an influence that can cause an object to change its velocity, i.e., to accelerate, unless counterbalanced by other forces. Is that clear? Well you won't really know until you do some examples. So we can draw the vectors head to head, to subtract them. I'm going to add B to something to get A. So if D = A- B, then D is what I have to add B to to get A. Here's another way, when I say 7- 4 = 3 I mean that 3 is what I have to add to 4 to get 7. So here's a diagram of A + (-B), that's one easy way to subtract vectors. B is five meters east, so (-B) is five meters west. Well, what about A- B, how do we subtract vectors? There are two ways. So when we represent A and B with arrows, we simply add them by putting them head to tail. 5 meters squared plus 5 meters squared equals 7 meters. Pythagoras' theorem gives us the magnitude of the new displacement. Our new displacement is northeast of our starting point. Okay, let's go five meters north, turn a right angle and five meters east. They're examples of what we call unit vectors. They have a direction and their magnitude is one. In this context I've actually written north, and east as vectors because they are. The length of the arrow represents the magnitude of the vector. Suppose vector A is five meters north, and vector B is five meters east. Adding and subtracting vectors is more complicated. All you have do is to remember to get the units right, then do the arithmetic. Adding and subtracting scalars is simple. Vectors have both magnitude and a direction. Scalars have magnitude of size, but no direction. I'd certainly notice the difference when I go to look for my pen. If I displace it 30 centimeters south that is a different displacement. In contrast, 30 centimeters east is a displacement. Of course, the magnitude of velocity must have dimensions of distance per unit time. And the magnitude of a vector is indeed a scalar. The two vertical lines mean the magnitude of a vector. The second cannot be true, because a vector cannot equal a scalar. We have a vector on both sides of the equation. When we specify a vector, we must give magnitude and direction. Some people put an arrow above the vector in handwriting and in printing vectors are often given bold functions. For velocity I write V with a wiggly line below, that indicates its a vector. In handwriting a normal letter V is the speed which is the scalar. A velocity of 1 meter per second east is no good if you want to go north. Velocity is a vector, it has magnitude and direction. Speed is an example of what we call a scalar quantity. Meanwhile, we think you'll have some fun, too. However, we do provide a study aid introducing the calculus that would accompany this course if it were taught in a university.īy studying mechanics in this course, you will understand with greater depth many of the wonders around you in everyday life, in technology and in the universe at large. You will need some high-school mathematics: arithmetic, a little algebra, quadratic equations, and the sine, cosine and tangent functions from trigonometry. You'll do a range of interesting practice problems, and in an optional component, you will use your ingenuity to complete at-home experiments using simple, everyday materials. The course uses rich multimedia tutorials to present the material: film clips of key experiments, animations and worked example problems, all with a friendly narrator. (The survey tells us that it's often used by science teachers, too.) This on-demand course is recommended for senior high school and beginning university students and anyone with a curiosity about basic physics. This allows us to analyse the operation of many familiar phenomena around us, but also the mechanics of planets, stars and galaxies. Mechanics begins by quantifying motion, and then explaining it in terms of forces, energy and momentum. Most of the phenomena in the world around you are, at the fundamental level, based on physics, and much of physics is based on mechanics.
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