The scalar is a physical quantity that has an expression through a single module and its value is the same for all. Scalar and vector quantities have a numerical representation within a reference frame.
A physical quantity is considered scalar when it is presented with a unique number, that is, a single coordinate. The temperature of any body is always presented through a scalar magnitude, this means that a scalar is the mass of a body , because a number is sufficient to express it, such as: 20 kilograms.
Concepts of scalar and vector quantities
Scalar quantities are those perfectly determined by their unit and the value of their measure . Other magnitudes require a sense and a direction to be fully defined, this type of magnitude is called vector.
Actually, the concept of magnitude is related to any chemical or physical property that can be measured. Procedurally, the measure contracts a comparison with a defined quantity that serves as a reference and is called the unit-pattern.
Differences between fundamental quantities, such as mass, temperature, length, intensity of electric current, time, quantity of substance, and light intensity, give rise to the so-called derived quantities.
It can be said that the classes of quantities can be differentiated according to their elements, into scalar quantities and vector quantities.
Scalar quantities are all those that are adequately defined with the unit and the corresponding number. They are example the volume , temperature, pressure and energy.
Regarding vector magnitudes, it is said that for a total definition, a part of the corresponding unit plus a number is required, which specifies a direction having a sense of application. The vector magnitudes take different values for those who observe.
This means that speed as well as acceleration is a vector quantity. Vector quantities are graphically represented by vectors that are made up of segments oriented by an arrowhead.
Elements that make up the vector
- Modulus : represented by the numerical value of the large-scale magnitude.
- Direction : it is constituted by a line to which the vector belongs.
- Direction : defined as the orientation followed by the vector plotted by the tip of an arrow.
- Application point : represents the origin of the vector.
It is important to note that a vector magnitude is almost always graphed by adding an arrow above the letter that serves as its symbol.
Examples of scalar and vector quantities
Among the examples of scalar quantities, the following stand out:
- The length of a thread
- The passage of time between a duplication of events
- The mass that constitutes a body
- Density, power , volume, temperature, and mechanical work
These representations can be made by means of segments, placed on top of a line starting from its origin and with a length similar to the real number that its measurement shows.
Other examples of scalar quantities
It is worth mentioning the following:
- Temperature : this lacks direction because it is not a vector. It has a numerical value that defines it, such as the room temperature that is defined in degrees centigrade.
- Pressure : ambient pressure is the weight that the atmospheric air mass exerts on things, within a linear scale.
- Length: the distance between things is a relevant dimension that is measured through the metric system.
- Energy: it is customary to measure it in joules and it is the ability of matter to act physically or chemically.
- Mass : represents the amount of matter that an object has and is measured with the help of the metric system in units, such as: gram, kilogram or ton.
- Time : this has no direction or sense, it is a measurable scalar through the linear system.
- Area : it is represented by a figure that is expressed in square meters.
- Volume : is the space occupied by a body and is measured in cubic centimeters.
- Frequency: it is the one that allows to measure the number of repetitions of an event that has occurred per unit of time elapsed.
- Density: represents the relationship between the mass of a body and the volume it occupies.
Examples of vector quantities:
- The speed that a mobile can have at a point in space, for which it is necessary apart from its intensity, to indicate the direction of the movement, this is offered by the tangent line directed to the trajectory of each point, taking into account the movement that it happens in that direction.
- The acceleration, the angular momentum, the momentum or quantity of the movement. If you want to represent oriented segments, that is, certain line segments between extreme points that obey an established order, must be used.
- The modulus of a vector is always a positive number.
- The equal or team-lensing vectors have the same direction, the same module and the same sense.
In addition, free vectors are called those that slide along the path of a line, moving parallel in space. These vectors have 3 properties (symmetric, transitive and reflective).
Other examples of vector quantities
They are between them:
- Weight : is the force exerted by a certain object on a point of support. It is represented through the gravity of the object and towards the central part of the earth.
- Force : force is an element capable of changing the position, quantity or form of an object’s movement. Force is a vector.
- Acceleration : expresses the variation in speed, due to the unit of time.
- Speed : represents the amount of distance traveled by an object in a given unit of time.
- Torque : dictates the change of direction measure of a vector towards a curvature, allows the calculation of the speeds and rhythms of a lever.
- Position : is the location of a particle in space-time.
- Electrical voltage: referred to the voltage, composed of a flow of electrons that needs a vector logic to manifest.
- Electric field : they are those that describe the electric forces and the path to follow.