20 Examples of Vector and Scalar Quantities

It is called magnitudes to the measurable (measurable) physical attributes of objects or the interactions between them, such as forces, temperature, length, electrical charge, or many other variables. Depending on certain characteristics, the quantities can be of two types: scalars and vector.

The scalar quantities They are those that can be represented by a numerical scale, in which each specific value shows a greater or lesser degree of the scale. For instance: temperature, length.

The vector magnitudesInstead, they involve much more information than can simply be represented in a figure and also require a specific sense or direction within a given reference system. For instance: speed, force. For that, a vector as a representation of the unique sense of magnitude. Every vector is defined by four properties:

  • Application point. The place where the vector is “born”. This defines the reference system used to define the vector.
  • Address. The orientation with respect to an axis of the chosen reference system.
  • Sense. Towards which side of the action line the vector is directed.
  • Module. The length of the vector.

Examples of scalar quantities

  1. Temperature. It is a scalar quantity since a numerical value defines it completely. Temperature has no direction or sense, it is not a vector. For example: the room temperature is usually defined as 20 ºC.
  2. Pressure. Ambient pressure, usually measured in millimeters of mercury (mmHg), is the weight that the mass of air in the atmosphere exerts on things and is measurable on a linear scale. It has no direction or meaning, therefore it is not a vector.
  3. Length. The length of things or distances is one of the two fundamental dimensions, perfectly measurable through the linear scale of the metric or Anglo-Saxon system: centimeters, meters, kilometers, or yards, feet, inches.
  4. Energy. Defined as the ability of matter to act physically or chemically, it is usually measured in joules, although depending on the specific type of energy it can vary to other units (calories, therms, horsepower per hour, etc.), all scalars.
  5. Mass. The amount 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.
  6. Weather. Relativities aside, time is measurable through the same linear system of seconds, minutes, and hours. Time has no direction or meaning, so it is a scalar and not a vector.
  7. Area. Usually represented by a figure with units of square meters (m2), it is the surface that an enclosure or object occupies.
  8. Volume. It is the three-dimensional space occupied by a body and can be measured, for example, in meters or cubic centimeters (m3 or cm3).
  9. Frequency. It is a quantity that allows to measure the number of repetitions of a phenomenon or periodic event per unit of elapsed time. Its scalar unit is the hertz (Hz), which respond to the formulation 1Hz = 1 / s, that is, one repetition per second.
  10. Density. Density is the relationship between the mass of a body and the volume it occupies, the unit of density can be expressed in kilograms per cubic meter (kg / m3).

Examples of vector quantities

  1. Weight. Weight is a quantity 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 of the object generating gravity. It is a vector because it has a magnitude (m * g), a direction (the line that goes from the object’s center of gravity to the center of the Earth) and a direction (towards the center of the Earth).
  2. Strength. A force is understood to be anything capable of modifying the position, shape or amount of movement of an object or a particle. Force is a vector because, in addition to a magnitude (an intensity), a direction and a sense are needed to describe a force.
  3. Acceleration. This vector quantity expresses the change in speed per unit of time. An acceleration always has a direction and a sense, it is not the same to positively accelerate (go faster and faster) than to brake. The difference is expressed as a change of direction in the acceleration vector.
  4. Speed. It expresses the amount of distance traveled by an object in a given unit of time. Like acceleration, speed always requires a direction and sense to define it.
  5. Torsion. Also called “torque”, it expresses the measure of change of direction of a vector towards a curvature, so it allows calculating the speeds and rates of rotation, for example, of a lever. Therefore, it merits vector positioning information.
  6. Position. This magnitude refers to the location of a particle or object in space-time. To define a position you need to know a distance and its direction with respect to an axis. For example, Chile is some distance from Argentina to the west and Sydney some distance to the east. Without the address data the position is not completely defined.
  7. Electric tension. Also known as voltage, electrical voltage is the difference in electrical potential between two points or two particles. As it depends directly on the path of the charge between the initial and final points, that is, a flow of electrons, it requires vector logic to be expressed.
  8. Electric field. Electric fields describe electric forces. Forces are vectors, so fields are too.