Concept of Kinematics and examples

This article will be about The basic concept of kinematics, with examples where we can find a better way to understand the motion study, besides the types of motion.

Kinematics definition

The kinematics is a branch of physics and part of mechanic that studies the motion of an object without considering the causes of the motion (the forces) that makes the object move. In kinematics there are causes of the motion but only in velocity and acceleration level, for example, to move a shopping kart we have to apply a force to make it move, but in the motion study the causes of the motion are the accelerations and velocities produced by the force.

The main objective of the kinematics is to study the trajectory of a moving object, this to predict the position of the object in every moment, but, even when the trajectory is the main objective, we are also going to study other factors that affect the movement of an object one way or another. The distance or position, the velocity, the acceleration and the time are the physical magnitudes in which this study is based, where every magnitude is affected by each other, for example, the acceleration defines the change of the velocity, and the velocity makes that an object advances more or less, what this magnitudes have in common is that this magnitudes change depending on the time.

Conceptos y magnitudes fisicas en la Cinemática

The acceleration defines the variation of the velocity, and in real examples the acceleration can be applied by an engine, or the legs of a person when starting to run, but, an acceleration that every body on earth has is the gravity, this is a force that makes the bodies accelerate down (this is what keeps us stick into earth) and its approximated value is 9.8 m/s².

Both acceleration and velocity are vector magnitudes, this means that they cannot be represented only by one number, like we could do with the distance, the distance could be expressed in only one number, in kilometers, miles, etc, but the acceleration and the velocity are not like the distance. The acceleration and velocity vector besides of having a magnitude (which is the main value) also has a direction, this is because when we have a velocity or an acceleration, we have to know where is it pointing to, in the case of the gravity, as we explained it has a magnitude of 9.8m/s², but as we know the gravity points down, and this is the direction of the gravity.

The kinematics and the dynamic are two studies that are connected, because the kinematics is the pure study of the motion, and the dynamic is the same as kinematics but, with the forces causing the motion, so it is important to understand how are this studies developed so we can combine this studies easily.

Examples of kinematics

Any movement can be study in kinematics, some of them are a little more complex then the others, but all of them are study by the kinematics, here is a list of some of the most common ones:

In brakets is the type of motion of the examples.

The movement of a car in a straight line (constant velocity motion)
Somebody skydiving (Free fall)
*An apple that falls from a tree (free fall)
A rocket flying towards space (vertical motion)
A plane flying (uniform accelerated motion)
A 3 shot points in basketball (projectile motion)
The plate of a microwave (uniform circular motion)
A car accelerating from 0 (uniform accelerated motion)
A freekick of a soccer player (projectile motion)
The movement of the blades of a fan (uniform circular motion)
The trajectory of a wrecking ball (uniform circular motion)
A ball being throw in baseball(projectile motion)
The constant movement of a clock hand (uniform circular motion)
The helicopter proppelers when the engine starts (non uniform circular motion)
The movement of fireworks (Vertical motion)
A cheetah running at its fastest speed for a few seconds (constant velocity motion)
A glass that falls from a table (Free fall)

A very famous example is the newton´s apple (even when we do not know if the apple actually hit newton´s head or If he only saw it fall from the tree), this is an example of a free fall and it was one of the first studies of the motion, and it was a key piece for the physics we have today.

Motions in kinematics

There are some types of motions that are part of the kinematics, this are classified depending on the type of acceleration and trajectory that each of this have, because there are some motions that does not have any acceleration, or that the direction of the velocity changes constantly. For each of this motions there are equations or formulas that allows as understand the motions and the relations between the magnitudes. Although there are some equations of some motions that are similar to other motions and only changes a few factors, this are divided by the quantity of dimensions the object moves on, because there are some motions that moves only on in dimension, others that move in two dimension or tree dimensions.

Types of motions

Constant velocity motion Uniform accelerated motion Projectile motion Free fall Vertical motion Uniform circular motion Non uniform circular motion

Motions like the uniform circular motion and the non uniform circular motion are part of the rotational kinematics, that in general this motions are common in particles or objects that move around an edge, this are a little more complex, because there are some more types of velocities and accelerations related to the rotation of the object, as it can be the angular and tangential velocities and accelerations. While the rest of the motions that moves on a straight line are part of the linear kinematics.

The motions we showed before are only in one or two dimensions but there is also a 3d kinematics.

Reference Systems

A reference system is a way to represent the motion from a static point of view, this is useful to calculate the physical magnitude appreciated from a reference point, this is because the physical magnitudes are relative, because a motion seen from different points of view could change everything.

For example if a person walks along a bus in movement and we would take two reference points, one inside the bus and the other one on the ground, we would see two different motions, the reference inside the bus would appreciate that this person is walking at the velocity that is walking, but the reference point on the ground would see that this person is walking at the velocity of the bus plus the velocity of the person.

The previous examples show that the same movement can look very different if it is seen from different perspectives, this is why why always have to use a reference system in kinematics.

A reference system can be represented on a Cartesian plane, it can be either two-dimensional or three-dimensional.

Classical and relative Kinematics

The difference between this two parts is that in the classical kinematics they use to believe that some magnitudes were constants, for example in case of the time, before they use to believe that a second on earth would be the same than a second at the other side of the universe traveling at an extremely high speed, but this changed with Einstein´s relativity, where he showed that not even the time was constant in the whole universe, what can be like a second for somebody that is at rest could be a lot less time for somebody that is traveling at a super high speed, this is why some things changed in kinematics, because now we have to work with the relativity, and it was called relative kinematics.