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- High School Physics : Understanding Scalar and Vector Quantities
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Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. Scalar quantities that have the same physical units can be added or subtracted according to the usual rules of algebra for numbers. When we multiply a scalar quantity by a number, we obtain the same scalar quantity but with a larger or smaller value.

Two scalar quantities can also be multiplied or divided by each other to form a derived scalar quantity. For example, if a train covers a distance of km in 1. Many physical quantities, however, cannot be described completely by just a single number of physical units. For example, when the U. Coast Guard dispatches a ship or a helicopter for a rescue mission, the rescue team must know not only the distance to the distress signal, but also the direction from which the signal is coming so they can get to its origin as quickly as possible.

Physical quantities specified completely by giving a number of units magnitude and a direction are called vector quantities. Examples of vector quantities include displacement, velocity, position, force, and torque.

We can add or subtract two vectors, and we can multiply a vector by a scalar or by another vector, but we cannot divide by a vector. The operation of division by a vector is not defined.

Analytical methods are more simple computationally and more accurate than graphical methods. From now on, to distinguish between a vector and a scalar quantity, we adopt the common convention that a letter in bold type with an arrow above it denotes a vector, and a letter without an arrow denotes a scalar. For example, a distance of 2. Suppose you tell a friend on a camping trip that you have discovered a terrific fishing hole 6 km from your tent.

It is unlikely your friend would be able to find the hole easily unless you also communicate the direction in which it can be found with respect to your campsite. Displacement is a general term used to describe a change in position, such as during a trip from the tent to the fishing hole. Displacement is an example of a vector quantity. The arrowhead marks the end of the vector. Suppose your friend walks from the campsite at A to the fishing pond at B and then walks back: from the fishing pond at B to the campsite at A.

In Figure 2. Two vectors that have identical directions are said to be parallel vectors —meaning, they are parallel to each other. Two vectors with directions perpendicular to each other are said to be orthogonal vectors. Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, indicate whether their velocity vectors are equal or otherwise. Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors.

If he walks only a 0. All of this can be stated succinctly in the form of the following vector equation :. In a vector equation, both sides of the equation are vectors. In a scalar equation, both sides of the equation are numbers.

Now suppose your fishing buddy departs from point A the campsite , walking in the direction to point B the fishing hole , but he realizes he lost his tackle box when he stopped to rest at point C located three-quarters of the distance between A and B, beginning from point A.

So, he turns back and retraces his steps in the direction toward the campsite and finds the box lying on the path at some point D only 1. The vector sum of two or more vectors is called the resultant vector or, for short, the resultant. The direction of the resultant is parallel to both vectors. In general, in one dimension—as well as in higher dimensions, such as in a plane or in space—we can add any number of vectors and we can do so in any order because the addition of vectors is commutative ,.

When adding many vectors in one dimension, it is convenient to use the concept of a unit vector. The only role of a unit vector is to specify direction. In this way, the displacement of 6. Samuel J. Learning Objectives Describe the difference between vector and scalar quantities. Identify the magnitude and direction of a vector.

Explain the effect of multiplying a vector quantity by a scalar. Describe how one-dimensional vector quantities are added or subtracted.

Explain the geometric construction for the addition or subtraction of vectors in a plane. Distinguish between a vector equation and a scalar equation. Exercise 2. Alice moves north at 6 knots and Bob moves west at 6 knots. Alice moves west at 6 knots and Bob moves west at 3 knots.

Alice moves northeast at 6 knots and Bob moves south at 3 knots. Alice moves northeast at 6 knots and Bob moves southwest at 6 knots. Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots. Algebra of Vectors in One Dimension Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors.

Contributors and Attributions Samuel J.

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Vector , in physics , a quantity that has both magnitude and direction. Although a vector has magnitude and direction, it does not have position. That is, as long as its length is not changed, a vector is not altered if it is displaced parallel to itself. In contrast to vectors, ordinary quantities that have a magnitude but not a direction are called scalars. For example, displacement , velocity , and acceleration are vector quantities, while speed the magnitude of velocity , time, and mass are scalars.

VECTOR QUANTITIES IN. MECHANICS AND MOTION. ANALYSIS. CHAPTER objectives. To give students a good basic understanding of vectors and scalars.

In the study of physics, there are many different aspects to measure and many types of measurement tools. Scalar and vector quantities are two of these types of measurement tools. Keep reading for examples of scalar quantity and examples of vector quantity in physics. Understanding the difference between scalar and vector quantities is an important first step in physics.

Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. Scalar quantities that have the same physical units can be added or subtracted according to the usual rules of algebra for numbers. When we multiply a scalar quantity by a number, we obtain the same scalar quantity but with a larger or smaller value. Two scalar quantities can also be multiplied or divided by each other to form a derived scalar quantity. For example, if a train covers a distance of km in 1.

This is a list of physical quantities. The first table lists the base quantities used in the International System of Units to define the physical dimension of physical quantities for dimensional analysis. The second table lists the derived physical quantities. Derived quantities can be mentioned in terms of the base quantities. Note that neither the names nor the symbols used for the physical quantities are international standards. Some quantities are known as several different names such as the magnetic B-field which known as the magnetic flux density , the magnetic induction or simply as the magnetic field depending on the context.

Лицо его снизу подсвечивалось маленьким предметом, который он извлек из кармана. Сьюзан обмякла, испытав огромное облегчение, и почувствовала, что вновь нормально дышит: до этого она от ужаса задержала дыхание. Предмет в руке Стратмора излучал зеленоватый свет. - Черт возьми, - тихо выругался Стратмор, - мой новый пейджер, - и с отвращением посмотрел на коробочку, лежащую у него на ладони. Он забыл нажать кнопку, которая отключила звук. Этот прибор он купил в магазине электроники, оплатив покупку наличными, чтобы сохранить анонимность. Никто лучше его не знал, как тщательно следило агентство за своими сотрудниками, поэтому сообщения, приходящие на этот пейджер, как и отправляемые с него, Стратмор старательно оберегал от чужих глаз.

Сьюзан важно было ощущать свое старшинство. В ее обязанности в качестве главного криптографа входило поддерживать в шифровалке мирную атмосферу - воспитывать. Особенно таких, как Хейл, - зеленых и наивных. Сьюзан посмотрела на него и подумала о том, как жаль, что этот человек, талантливый и очень ценный для АНБ, не понимает важности дела, которым занимается агентство. - Грег, - сказала она, и голос ее зазвучал мягче, хотя далось ей это нелегко. - Сегодня я не в духе. Меня огорчают твои разговоры о нашем агентстве как каком-то соглядатае, оснащенном современной техникой.

- Голос послышался совсем. - Ни за. Ты же меня прихлопнешь.

ТРАНСТЕКСТ ежедневно без проблем взламы-вает эти шифры. Для него все шифры выглядят одинаково, независимо от алгоритма, на основе которого созданы. - Не понимаю, - сказала .

Итак, где ключ. Хейл попытался пошевелить руками, но понял, что накрепко связан. На лице его появилось выражение животного страха. - Отпусти. - Мне нужен ключ, - повторила Сьюзан.

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