Scalar And Vector Quantities Pdf

scalar and vector quantities pdf

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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.

Examples of Vector and Scalar Quantity in Physics

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Scalars, Vectors and Fields. Shahbaz Ahmed Alvi. Download PDF. A short summary of this paper. Scalars Scalars are those quantities which can be defined by a single number. It just tells you how much of something there is.

Other examples of scalar quantities are, energy, work done, electrical resistance etc. A scalar quantity is only represented by a letter or a symbol. Vectors Quantities categorized as vectors have a magnitude along with a direction.

In 3 dimensions you need 3 numbers to define a vector completely. These 3 numbers are called components of the vector in each of the three directions. Examples of vector quantities include velocity, acceleration, current density, area etc. Vector Products A vector can be multiplied in three ways. Product with a scalar.

When a vector is multiplied with a scalar, you get a new vector whose components, and magnitude, are greater than the original vector. A 3 dimensional vector A components. Product with a vector: Dot Product. It is also called a scalar product. Product with a vector: Cross Product. A cross product is when a vector is multiplied to another vector and the result is a vector. Fields A Field is basically a space a volume or a section of space where at every point some quantity is defined means some quantity has some value.

If this quantity is a scalar, the field is called a Scalar field. If the quantity is a vector the field is called a Vector field. So if you have temperature defined at every point in, for example, a room then the room represents a temperature scalar field. Similarly air molecules flowing in a pipe have velocity vector pointing in the direction of flow. If you plot the velocity vectors of molecules in the pipe, you got yourself a velocity vector field within the pipe.

Plotting a field. Plotting a scalar field is simple. You have a scalar function, which looks like any other mathematical function, and you plot that function at every point in the given space. A vector field is plotted is a similar way but at every point, in addition to a number, there is a vector with a direction. A vector function looks like any other vector. Everywhere in the space the vector has fixed direction and a fixed magnitude length! Which is pretty boring. Things get more interesting and admittedly attractive if the components of the field are not fixed but are variables i.

These vector fields will look like fig. Directional Derivative 5. Partial Derivative. You have studied Calculus in your previous Mathemat- ics classes and are equipped with the idea of differentiation. But functions that you used to differentiate depended only on one variable i.

Many functions in Mathematics and Physics depend on more than one variable i. The idea behind a partial derivative is to change only one variable at a time while keeping all the other variables constant. So if you are differentiating with respect to x, you will keep y and z constant.

Red shades show higher pressure and purple shades indicate low pressure. This is exactly what a partial derivative does; differentiates one variable at a time and keeps others constant. Directional Derivative. This operator gets its meaning when it operates on a scalar or a vector function. The direction and magnitude of the field varies b Vector field defined by V in space in the xy plane. For example, the picture shows the electric field of a point charge for which the divergence is maximum.

If the field is coming out at a point the divergence is positive and if it is going in then it is negative. The former is called the source of the field and the later is called the sink.

Like any other dot product, divergence of a field is a scalar. Its hard to imagine but there are some field which Figure 3. One such example is the magnetic field.

For instance, look at the magnetic field of a bar magnet, how the field lines start at the north pole travel towards the south and then through the magnet and end at North again.

The field lines are clearly not ending anywhere. Such a field, where field lines form closed loops, is one example of a divergenceless field. Figure 4. Magnetic field lines of a bar magnet form closed loops.

Since it is a cross product curl of a vector field is a vector. If you rotate your fingers in the direction of the field lines your thumb will point in the direction of the curl vector. Lets evaluate the curl of the same vector field. I told you that field lines which for closed loops have zero divergence but they such lines have maximum curl. In normal circumstances Electric field lines do not have a curl i.

Electric field which is created as a result of alternating magnetic field form closed loops and thus have a non-zero curl. Changing magnetic field lines through a loop causes cir- cular electric field lines which causes current in the loop.

Related Papers. By Uzair Siddique. By dilshan nilusha. A Student's Guide to Vectors and Tensors. Introduction to Calculus. By George Misirlis. Download pdf. Remember me on this computer. Enter the email address you signed up with and we'll email you a reset link. Need an account? Click here to sign up.

Examples of Vector and Scalar Quantity in Physics

To better understand the science of propulsion it is necessary to use some mathematical ideas from vector analysis. Most people are introduced to vectors in high school or college, but for the elementary and middle school students, or the mathematically-challenged:. There are many complex parts to vector analysis and we aren't going there. We are going to limit ourselves to the very basics. Vectors allow us to look at complex, multi-dimensional problems as a simpler group of one-dimensional problems. We will be concerned mostly with definitions The words are a bit strange, but the ideas are very powerful as you will see. If you want to find out a lot more about vectors you can download this report on vector analysis.

Scalars and Vectors

Length of the arrow Tail head 9. Addition of vectors must be done by considering their directions. Sample Problem: Suppose a teacher walked from his house going to school and then back to his house 50 m east S. What is the total distance and displacement made by the teacher?

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.

Scalar and vector quantities are ubiquitous in physics. However, most physics texts at the undergraduate level provide only a brief description of their nature. This creates confusion for many: all magnitudes are scalars and any physical quantity with magnitude and direction is defined as vector.

Scalar and vectors in physics - I


Multiple Choice Questions On Vectors And Scalars Pdf

Delete Quiz. Form the dot product between the unit coordinate vectors. The position of a particle in a rectangular coordinate system is 3,2,5. Visualizing vectors in 2 dimensions. This is a good question.

Халохот рано принялся считать цыплят. - Но кровь… - Поверхностная царапина, мадам. Мы залепили ее пластырем. Сьюзан лишилась дара речи. Перед камерой появился агент Смит. - Мы выстрелили в него новым Джей-23, это нервно-паралитическое вещество продолжительного действия.

 - Слово разница особенно важно. Главная разница между Хиросимой и Нагасаки. По-видимому, Танкадо считал, что два эти события чем-то различались между. Выражение лица Фонтейна не изменилось. Но надежда быстро улетучивалась. Похоже, нужно было проанализировать политический фон, на котором разворачивались эти события, сравнить их и перевести это сопоставление в магическое число… и все это за пять минут. ГЛАВА 124 - Атаке подвергся последний щит.




Physics is a mathematical science.



Displacement is a vector while distance is a scalar quantity.

Madeleine P.


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