The scalar quantities are those representable by a numerical scale, in which each specific value accuses a greater or lesser degree of the scale. Eg temperature , length .
The vector quantities , however, involve much more information than simply representable in a figure, often requiring a specific sense of direction within a specified coordinate system. Eg speed , strength . To do this, a vector is imposed as a representation of the unique meaning of the magnitude. Every vector is governed by four fundamental coordinates:
- Point of application . The place where the vector “is born”. It’s usually a point.
- Address . The trajectory that follows. It is usually a straight line.
- Sense . The orientation of the magnitude along the specified path. Usually it is an arrowhead at the end of the straight line.
- Module. The degree of intensity of the vector.
Examples of scalar quantities
- Temperature . Depending on the scale used (Celsius or Kelvin), each numerical value will represent an absolute magnitude of (presence or absence of) heat, so that 20 ° C constitute a fixed value within the scale, regardless of the conditions that accompany the measurement.
- The pressure. The environmental pressure, usually measured in millimeters of mercury (mmHg) is the weight that the air mass of the atmosphere exerts things and is measurable through a linear scale.
- Length . One of the two fundamental dimensions, the length of things or distances, is perfectly measurable through the linear scale of the metric or Anglo-Saxon system: centimeters, meters, kilometers, or yards, feet, inches.
- Energy . Defined as the ability to act physically or chemically of matter, it is usually measured in joules, although depending on the specific type of energy can vary to other units (calories, thermies, horsepower per hour, etc), all scalars.
- The mass . The quantity of matter that an object contains is measured as a fixed value through the metric or Anglo-Saxon system of units: gram, kilogram, ton, pound, etc.
- Time . Relativities apart, time is measurable through the same linear system of seconds, minutes and hours, regardless of the conditions in which the measurement occurs.
- Area . Usually represented by a number of square meters (m 2 ) it is the surface area of an enclosure or an object, as opposed to what is around.
- The volume. Relationship of the three-dimensional space occupied by a specific body, measurable in cubic centimeters (cm 3 ).
- Frequency . It is a magnitude that allows to measure the number of repetitions of a phenomenon or periodic event per unit of time elapsed. Its scalar unit is the hertz (Hz), which respond to the formulation 1Hz = 1 / s, that is, one repetition per second.
- Density . The density is the relationship between the mass of a body and the volume it occupies, so it is a value dependent on both magnitudes, and can be represented by its own scale: Kilograms per cubic meter (kg / m 3 ) .
Examples of vector quantities
- Weight . The weight is a magnitude that expresses the force exerted by an object on a point of support, as a consequence of the local gravitational attraction. It is represented vectorially from the center of gravity of the object and towards the center of the Earth or from the object generating gravity . It differs from the mass because it is not an intrinsic property of the object, but gravitational attraction.
- Force . Force is understood as anything capable of modifying the position, shape or amount of movement of an object or a particle, expressed in newtons (N): the amount of force necessary to provide an acceleration of 1 m / s 2 to 1 kg of dough. However, it requires guidance and direction, since every force is exerted from one point to another.
- Acceleration . This vectorial magnitude expresses the variation of speed based on the course of a unit of time. Like speed, it requires a vectorial content incompatible with a numerical scale, since it uses referential values to express itself.
- Speed . Express the amount of distance traveled by an object in a given unit of time, noted as meters per second (mps). In order to measure the variation of the object’s position, it always requires a direction of movement and a module, which expresses its speed or speed.
- Torsion . Also called torque, it expresses the measure of change of direction of a vector towards a curvature, by which it allows to calculate the speeds and rates of rotation, for example, of a lever. Therefore, it deserves vector positioning information.
- Position . This magnitude refers to the location of a particle or object in spacetime. That is why its classical representation is vectorial, to express it in a plane of reference coordinates; while for relativity it is a set of arbitrary curvilinear coordinates, since the spacetime in that theory is curved.
- Voltage . Also known as voltage, the electrical voltage is the difference in electrical potential between two points or two particles. Since it depends directly on the path of the charge between the starting point and the end point, that is, a flow of electrons, it requires a vector logic to express itself.
- Electric field . It is a vectorial field, that is to say, a set or relation of physical forces (electrical in this case) that exert influence on a certain area and modify a determined electric charge in its interior.
- Gravitational field . Another physical field, but of gravitational forces that exert an attraction on the objects or particles that enter the area. Since all force is necessarily vector, the gravitational field will need a set of vectors to be represented.
- Inertia . The force of friction, opposed to all movement and always tending to stillness, expresses itself vectorially as it opposes the forces of movement, always tending to the same direction but opposite orientation.