The two words that frighten schoolchildren - vector and scalar - are not actually scary. If you approach the topic with interest, then everything can be understood. In this article we will consider which quantity is vector and which is scalar. More precisely, we will give examples. Every student probably noticed that in physics some quantities are denoted not only by a symbol, but also by an arrow on top. What do they mean? This will be discussed below. Let's try to figure out how it differs from scalar.
Examples of vectors. How are they designated?
What is meant by vector? That which characterizes movement. It doesn't matter whether in space or on a plane. What quantity is a vector quantity in general? For example, an airplane flies at a certain speed at a certain altitude, has a specific mass, and began moving from the airport with the required acceleration. What is the motion of an airplane? What made him fly? Of course, acceleration, speed. Vector quantities from a physics course are clear examples. To put it bluntly, a vector quantity is associated with motion, displacement.
Water also moves at a certain speed from the height of the mountain. Do you see? Movement is carried out not by volume or mass, but by speed. A tennis player allows the ball to move with the help of a racket. It sets the acceleration. By the way, attached to in this case force is also a vector quantity. Because it is obtained as a result of given speeds and accelerations. Strength can also change, exercise concrete actions. The wind that moves the leaves on the trees can also be considered an example. Because there is speed.
Positive and negative quantities
A vector quantity is a quantity that has a direction in the surrounding space and a magnitude. The scary word appeared again, this time module. Imagine that you need to solve a problem where a negative acceleration value will be recorded. In nature negative values, it would seem, does not exist. How can speed be negative? 
A vector has such a concept. This applies, for example, to forces that are applied to the body, but have different directions. Remember the third where action is equal to reaction. The guys are playing tug of war. One team wears blue T-shirts, the other team wears yellow T-shirts. The latter turn out to be stronger. Let us assume that their force vector is directed positively. At the same time, the first ones cannot pull the rope, but they try. An opposing force arises.
Vector or scalar quantity?
Let's talk about how a vector quantity differs from a scalar quantity. Which parameter has no direction, but has its own meaning? Let's list some scalar quantities below:
Do they all have a direction? No. Which quantity is vector and which is scalar can only be shown with visual examples. In physics there are such concepts not only in the section “Mechanics, dynamics and kinematics”, but also in the paragraph “Electricity and magnetism”. The Lorentz force is also a vector quantity.
Vector and scalar in formulas
Physics textbooks often contain formulas that have an arrow at the top. Remember Newton's second law. Force ("F" with an arrow on top) is equal to the product of mass ("m") and acceleration ("a" with an arrow on top). As mentioned above, force and acceleration are vector quantities, but mass is scalar.
Unfortunately, not all publications have the designation of these quantities. This was probably done to simplify things so that schoolchildren would not be misled. It is best to buy those books and reference books that indicate vectors in formulas. 
The illustration will show which quantity is a vector one. It is recommended to pay attention to pictures and diagrams in physics lessons. Vector quantities have a direction. Where is it directed? Of course, down. This means that the arrow will be shown in the same direction.
IN technical universities study physics in depth. In many disciplines, teachers talk about what quantities are scalar and vector. Such knowledge is required in the following areas: construction, transport, natural sciences.
13 signs you have the best husbandHusbands are truly great people. What a pity that good spouses don't grow on trees. If your significant other does these 13 things, then you can...
0 0
Marriage 
What happens to the body of a person who does not have sex?Sex is almost the same basic need as well as eating. At least once you start doing it, you won’t stop. Even if you adhere...
0 0
SexualityVector and scalar quantities
In physics, there are two types of physical quantities: vector and scalar. Their main difference is that vector physical quantities have a direction. What means physical quantity has a direction? For example, we will call the number of potatoes in a bag ordinary numbers, or scalars. Another example of such a quantity is temperature. Other very important quantities in physics have a direction, for example, speed; we must specify not only the speed of movement of the body, but also the path along which it moves. Momentum and force also have a direction, just like displacement: when someone takes a step, you can tell not only how far he has stepped, but also where he is walking, that is, determine the direction of his movement.
Coordinate system- a set of definitions that implements coordinate method , that is, a way to determine the position of a point or body using numbers or other symbols. The set of numbers that determine the position of a specific point is called coordinates this point.
Kinematics (Greekκινειν - move) in physics - section mechanics, studying mathematical description (by means geometry, algebra, mathematical analysis...) movements of idealized bodies ( material point, absolutely rigid body, ideal liquid), without considering the reasons for the movement ( masses, strength etc.). Basic concepts of kinematics - space And time. For example, if a body moves in a circle, then kinematics predicts the need for the existence centripetal acceleration without specifying what nature the force that generates it has. Causes of occurrence mechanical movement deals with another branch of mechanics - dynamics.
Trajectory of a material point- a line in space, representing a set of points at which a material point was, is, or will be located when it moves in space relative to the chosen reference system. . It is important that the concept of trajectory has physical meaning even in the absence of any movement along it. In addition, even in the presence of an object moving along it, the trajectory depicted in a predetermined system of spatial coordinates itself cannot say anything definite regarding the reasons for its movement until the configuration is analyzed fields of forces acting on it in the same coordinate system.
Acceleration(usually denoted in theoretical mechanics) - the rate of change of speed, that is, the first derivative of speed with respect to time, a vector quantity showing how much the velocity vector of a body changes during its movement per unit time:
Uniform movement - mechanical movement, in which the body travels the same distance in any equal periods of time. Uniform movement material point is a movement in which the magnitude speed point remains/unchanged. The distance traveled by the point in time is given in this case by the formula.
Equally alternating motion- movement with constant acceleration. Equations of uniform motion: 
.
Accelerationfree fall - acceleration, attached body gravity, with the exclusion of other forces from consideration. In accordance with the equation of motion of bodies in non-inertial reference systems acceleration of gravity numerically equal to the force of gravity acting on an object per unit masses.
Kinematics of rotational motion - a branch of kinematics that studies the mathematical description of motion material points. The main task of kinematics is to describe movement using a mathematical apparatus without identifying the reasons causing this movement
Absolutely solid body- second reference object mechanics along with material point. The mechanics of an absolutely rigid body is completely reducible to the mechanics of material points (with superimposed connections), but has its own content (useful concepts and relationships that can be formulated within the framework of the absolutely rigid body model), which is of great theoretical and practical interest.
Rotational movement- view mechanical movement. At rotational movement material point she describes circle. At rotational movement absolutely rigid body all its points describe circles located in parallel planes. The centers of all circles lie on the same straight line, perpendicular to the planes of the circles and called axis of rotation. The axis of rotation can be located inside the body or outside it. Axis rotation in this reference system can be either movable or immobile. For example, in the reference frame associated with Earth, axis of rotation rotor generator motionless at the power plant.
Tangential acceleration - component acceleration, directed along tangent To trajectories movements. Characterizes change module speed as opposed to normal component, characterizing the change in direction of speed
Centripetal acceleration- component acceleration point characterizing the speed of change in the direction of the velocity vector for a trajectory with curvature (the second component, tangential acceleration, characterizes the change in speed module)
the angle of rotation is not a geometric, but a physical quantity that characterizes the rotation of a body, or the rotation of a ray emanating from the center of rotation of the body, relative to another ray considered stationary.
Angular acceleration- pseudo-vector physical quantity characterizing the speed of change in the angular velocity of a material point. When the point rotates around a fixed axis, the angular acceleration in absolute value is equal to
Newton's first law postulates the existence of inertial frames of reference. Therefore it is also known as Law of Inertia. Inertia- this is the property of a body to maintain its speed of movement unchanged (both in magnitude and direction) when no forces act on the body. To change the speed of a body, it must be acted upon with some force. Naturally, the result of the action of forces of equal magnitude on different bodies will be different. Thus, they say that bodies have different inertia. Inertia is the property of bodies to resist changes in their speed. The amount of inertia is characterized mass bodies.
Newton's second law is a differential law of motion that describes the relationship between a force applied to a material point and the resulting acceleration this point. In fact, Newton's second law introduces mass as a measure of the manifestation of the inertia of a material point in the selected inertial frame of reference (IRS). The mass of a material point is assumed to be constant in time and independent of any features of its movement and interaction with other bodies
This law describes how two material points interact. Let us take for example a closed system consisting of two material points. The first point can act on the second with some force, and the second - on the first with force. How do the forces compare? Newton's third law states: the action force is equal in magnitude and opposite in direction to the reaction force.
Elastic force- a force that arises during deformation of a body and counteracts this deformation. In the case of elastic deformations, it is potential. The elastic force is of an electromagnetic nature, being a macroscopic manifestation of intermolecular interaction. In the simplest case of tension/compression of a body, the elastic force is directed opposite to the displacement of the particles of the body, perpendicular to the surface. The force vector is opposite to the direction of deformation of the body (the displacement of its molecules
Hooke's law In the simplest case of one-dimensional small elastic deformations, the formula for the elastic force has the form:
Where is the rigidity of the body, is the magnitude of the deformation. In its verbal formulation, Hooke’s law is as follows: The elastic force that arises during deformation of the body is directly proportional to the elongation of the body and is directed opposite to the direction of movement of particles of the body relative to other particles during deformation
Gravity (attraction, universal gravity, gravity) (from lat. gravitas- “heaviness”) - universal fundamental interaction between all material bodies.
Law of Gravity was formulated Isaac Newton(1643-1727) and published in 1687. In accordance with this law, two bodies are attracted to each other with a force that is directly proportional to the masses of these bodies m 1 and m 2 and is inversely proportional to the square of the distance between them:
Friction force is a force that arises at the point of contact of bodies and impedes their relative motion. Reasons for the occurrence of friction force: 1) Roughness of contacting surfaces. 2) Mutual attraction of the molecules of these surfaces.
Pulse (Quantity of movement) is a vector physical quantity that is a measure of the mechanical motion of a body. IN classical mechanics the momentum of a body is equal to the product of mass m of this body at its speed v, the direction of the impulse coincides with the direction of the velocity vector:
Law of conservation of momentum (Law of conservation of momentum) states that the vector sum impulses of all bodies (or particles) of the system is a constant value if the vector sum of external forces acting on the system is equal to zero.
Mechanical work- This physical quantity, which is scalar quantitative measure of action strength or forces on a body or system, depending on the numerical magnitude, direction of the force (forces) and on the movement of the point (points), body or system
Kinetic energy - energy mechanical system, depending on speeds movement of its points in the selected reference system. Often release kinetic energy progressive And rotational movement
A force is said to be potential if there is a scalar function of coordinates, known as potential energy and denoted by , such that
Law of energy conservation- fundamental law nature, established empirically and which consists in the fact that for isolated physical system a scalar can be introduced physical quantity, which is function system parameters and called energy, which persists over time time. Since the law of conservation of energy does not apply to specific quantities and phenomena, but reflects a general pattern that is applicable everywhere and always, it can not be called by law , A principle energy conservation
Absolutely inelastic blow- an impact, as a result of which the velocity components of bodies normal to the contact area become equal. If the impact was central (the velocities were perpendicular to the tangent plane), then the bodies connect and continue their further movement as a single body.
Absolutely elastic impact- collision model in which complete kinetic energy system is saved. IN classical mechanics in this case, the deformations of the bodies are neglected. Accordingly, it is believed that energy is not lost due to deformation, and the interaction spreads throughout the body instantly
Harmonic vibrations- oscillations in which a physical (or any other) quantity changes over time according to a sinusoidal or cosine law. The kinematic equation of harmonic oscillations has the form.
Spring pendulum- a mechanical system consisting of a spring with elasticity coefficient (rigidity) k ( Hooke's law), one end of which is rigidly fixed, and on the other there is a load of mass m.
Quasi-elastic force directed towards the center O force F, the value of which is proportional to the distance r from center O to the point of application of force; numerically F = cr, Where With - constant coefficient. A body under the influence of cosmic energy has a potential energy P = 1/2 cr 2 .
Molecular kinetic theory(abbreviated as MKT) is a theory that arose in the 19th century and considers the structure in 
substances, mainly gases, from the point of view of three main approximately correct provisions
Basic MCT equation for an ideal gas. Derived on the assumption that gas pressure is the result of impacts of its molecules on the walls of the vessel.
Internal energy thermodynamic system (denoted as E or U ) is the sum of the energies of thermal motion of molecules and intermolecular interactions. In axiomatic thermodynamics, the movement of molecules is not considered, and the internal energy of a thermodynamic system is defined as a function of the state of the system, the increment of which in any process for an adiabatically isolated system is equal to work external forces when the system transitions from the initial state to the final state
The amount of heat is not a function of state, and the amount of heat received by a system in any process depends on the manner in which it was transferred from the initial state to the final state. The unit of measurement in the International System of Units (SI) is the joule. The calorie is also used as a unit of heat measurement. In the Russian Federation, the calorie is approved for use as a non-systemic unit without a time limit with the scope of application “industry”.
First law of thermodynamics- one of the three fundamental laws thermodynamics, represents law of energy conservation For thermodynamic systems. Quantity of heat, received by the system, is used to change it internal energy and doing work against external forces
Specific heat capacity is called the heat capacity per unit amount of a substance. The amount of a substance can be measured in kilograms, cubic meters and moles.
Molar heat capacity (WITHμ) is the amount of heat that must be brought to 1 I pray substance to heat it per unit temperature. In SI it is measured in joules per mole per kelvin (J/(mol K))
Internal energy is the kinetic energy of the chaotic (thermal) movement of particles of a system (molecules, atoms, nuclei, electrons) and the potential energy of interaction of these particles. The internal energy of an ideal gas is the sum of the kinetic energies of its particles (we neglect the interaction energy of particles).
Evaporation. This is a process in which molecules are ejected from the surface of a liquid or solid, the kinetic energy of which exceeds the potential interaction energy of the molecules. Evaporation is accompanied by cooling of the liquid.
Saturated and unsaturated steam. The evaporation of a liquid in a closed vessel at a constant temperature leads to a gradual increase in the concentration of molecules of the evaporating substance in the gaseous state. Some time after the start of the evaporation process, the concentration of the substance in the gaseous state reaches a value at which the number of molecules returning to the liquid per unit time becomes equal to the number of molecules leaving the surface of the liquid during the same time. A dynamic equilibrium is established between the processes of evaporation and condensation of the substance. The pressure of an ideal gas at a constant concentration of molecules increases in direct proportion to the absolute temperature. Since in saturated steam the concentration of molecules increases with increasing temperature, the pressure of saturated steam with increasing temperature increases faster than the pressure of an ideal gas with a constant concentration of molecules Boiling. Dependence of boiling temperature on pressure. The process of evaporation can occur not only from the surface of the liquid, but also inside the liquid. Vapor bubbles inside a liquid expand and float to the surface if the pressure saturated steam equal to or greater than external pressure. This process is called boiling.
Relative humidity. In atmospheric air, the rate of water evaporation depends on how close the water vapor pressure is to the saturated vapor pressure at a given temperature. Pressure ratio p water vapor contained in the air at a given temperature to pressure p 0 saturated water vapor at the same temperature, expressed as a percentage, is called relative air humidity.
Dew point. Since the pressure of saturated vapor is lower, the lower the temperature, when the air is cooled, the water vapor in it becomes saturated at a certain temperature. Temperature t p at which the water vapor in the air becomes saturated is called dew point.
Characteristic liquid state of things. Liquids occupy an intermediate position between gaseous and solid substances. At temperatures close to boiling points, the properties of liquids approach those of gases; at temperatures close to the melting point, the properties of liquids approach the properties of solids. If for solids characterized by strict ordering of particles, extending over distances of up to hundreds of thousands of interatomic or intermolecular radii, then in a liquid substance there are usually no more than several tens of ordered particles - this is explained by the fact that the order between particles in different places liquid substance arises just as quickly
Wetting- This superficial phenomenon, which consists in interaction liquids with surface solid or other liquid. The degree of wetting is characterized by the contact angle. The contact angle (or contact angle) is the angle formed by the tangent planes to the interfacial surfaces limiting the wetting liquid, and the apex of the angle lies on the line of separation of the three phases. Measured by the sessile drop method . In the case of powders, reliable methods give high degree reproducibility, has not yet been developed (as of 2008). A gravimetric method for determining the degree of wetting has been proposed, but it has not yet been standardized.
The equationLaplace- partial differential equation. In three-dimensional space, Laplace's equation is written as follows:
capillary effect- a physical phenomenon consisting of the ability liquids change the level in tubes, narrow channels of arbitrary shape, porous bodies. In the field of gravity (or inertial forces, for example, when centrifuging porous samples), liquid rise occurs in cases wetting channels with liquids, for example water in glass tubes, sand, soil, etc.
Solid- this is one of four states of matter, different from other states of aggregation ( liquids, gases, plasma) stability of form and character thermal movement atoms, committing small fluctuations near equilibrium positions ,"en":["rcDXQ-5H8mk","EUrMI0DIh40","rcDXQ-5H8mk","_W7i9Mj8_ms","EUrMI0DIh40","ihNZlp7iUHE","LMAB4MZR8LA","OY8_-FfZZQ0","2IICsTdFtxc","rcDXQ -5H8mk","_W7i9Mj8_ms","8WThnNzPsvo","8WThnNzPsvo"],"de":["wcjuKXcdwIk","saIGsRPUxYM","wcjuKXcdwIk","saIGsRPUxYM","saIGsRPUxYM"],"es":["DBi2K7K9VYQ ","r0DX7JWnqvs","2d-gv__8_IU","DBi2K7K9VYQ","DBi2K7K9VYQ","qvw7j9eKGdg ","DBi2K7K9VYQ","N1sZsv9I8Kw","7Q6i5-5dbmQ","dNdCqkZlfjY","_2hhrQIXL_w" "IN3Vikbyny4", "DBi2K7K9VYQ"],"pt":["98sMzk4rzR0","Q2MH_fOUSgM","98sMzk4rzR0","D4WXbxzau 6I","Q2MH_fOUSgM","FshgJsOlfxY","D4WXbxzau6I","D4WXbxzau6I"],"fr":["9RGflY pqUj4 ","2Bivr2yP0WM"],"it":["RLqVNIOd8m0","4Ub2dLrfaqs","iV8mTUFOq4w","L44sLnv3KCQ"],"cs":["0HzLhTK8emQ","0HzLhTK8emQ","0HzLhTK8emQ","0HzLhTK8emQ"] ,"pl":["0c5Cva7pN78","MMyZdj_ab3U","Z0O_et75pcc","Z0O_et75pcc","NSVcm13HOeA"],"ro":["7-B4mwBgVEc"])