# kinematics

2022

We explain what kinematics is and what is the origin of this branch of physics. Elements of kinematics and application examples.

physical that studies the movement of solid objects and their trajectory as a function of time, without taking into account the origin of the forces that motivate it. For this, the speed is taken into consideration (the change in the displacement per unit of weather) and the acceleration (change in speed) of the moving object.

The origins of kinematics go back to astronomy ancient times, when astronomers and philosophers like Galileo Galilei observed the movement of spheres in inclined planes and in free fall to understand the movement of the stars celestial. These studies, together with those of Nicolás Copernicus, Tycho Brahe and Johannes Kepler, served as a reference for Isaac Newton to formulate his three Laws of motion, and all this together founded modern kinematics at the beginning of the 18th century.

The contributions of the French Jean Le Rond d’Alembert, Leonhard Euler and André-Marie Ampère were key in establishing this discipline, baptized by Ampère himself as kinematics (from the Greek kinein, scroll, move).

The much later postulation of relativity by Albert Einstein would turn this discipline around and found relativistic kinematics, in which time and space They are not absolute dimensions, as the speed of light.

## Elements of kinematics

The basic elements of kinematics are three: space, time and a mobile. We must take into consideration that in the mechanics classical the first two (time and space) are absolute dimensions, independent of the mobile and prior to its existence.

Space is described by Euclidean geometry, time is considered unique in any region of the universe, and a mobile can be any body in motion. The simplest mobiles are particles (and its study opens the field of particle kinematics), but more frequently rigid solids (analogous to a system of particles and corresponding to what we know as bodies or objects) are considered.

In this sense, classical kinematics contemplates the following types of movement:

• Uniform line movement. A body travels at a constant speed v, with zero acceleration in a straight line.
• Uniformly accelerated rectilinear motion. A body moves at a speed that varies linearly (since its acceleration is constant) as time progresses.
• Simple harmonic movement. It is a periodic reciprocating motion in which a body oscillates around an equilibrium point in a address determined and in regular units of time.
• Parabolic movement. It is the composition of two different rectilinear movements: one horizontal and of constant speed, and the other vertically and uniformly accelerated.
• Uniform circular motion. As its name indicates, it is the movement that traces perfect circles in its path, keeping the modulus of its speed unchanged over time.
• Uniformly accelerated circular motion.It is the movement that traces perfect circles in its path, but with a speed that varies in module over time.
• Complex harmonic motion. It is the combination of various simple harmonic movements, in different directions.

## Examples of kinematics

The hands of a clock illustrate uniform circular motion.

Most of the known motions on the face of the earth are good examples from kinematics studies. The fall of a body, for example, is a movement uniformly accelerated by the force of gravity that Earth exerts on all objects. This force is what we call weight and points to the center of the planet.

Another example is a body suspended from an elastic, such as a spring, whose movement will be simple or complex harmonic depending on the forces we exert on it.

Finally, the movement of the hands of the clock or of a loose object inside a centrifuge (the clothes in the washing machine, for example), allows to illustrate the uniform or accelerated circular movement, respectively.

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