Study Material

# What is kinematics?

We explain what kinematics is, what it studies, its principles and we give several examples

## What is kinematics?

The kinematics is the branch of classical physics that deals only with the description of the motion of bodies without taking into account the interactions that led to this movement.

The movement of a body in general can be divided into two: a translation movement and a rotational movement. But if the object is small enough, almost tending to a point, then the motion is only translational, which is why the concept of a particle is useful in physics.

In physics, a particle is a material point, that is, a point with mass. The description of the motion of a large body can be complex, but it is simplified a lot if we consider a point called the center of mass, since this point behaves as if all the mass were concentrated in it.

If the object is symmetric and homogeneous, the center of mass coincides with its geometric center.

For example, the translational motion of the Moon relative to the Earth is the motion of the Moon’s center point. Similarly, if you wanted to describe the motion of a basketball, it suffices to describe the motion of its center of mass, a point that represents the translational motion of the entire ball.

Translational kinematics is the description of the motion of a material point of mass m, called “the particle.”

To locate the particle, a reference system is required , that is, a point from which the particle is observed.

Three mutually perpendicular axes, called Cartesian axes, pass through the origin of the reference system, which are used to define the position of a point in space by means of a coordinate system.

In addition to the system or frame of reference, the following kinematic quantities are defined, with which the movement is described:

• The position of the particle, at a given moment of observation, is the vector that starts from the origin of the reference system and goes to its location. This vector depends on the spatial coordinates, which in turn depend on time.
• Velocity is the next kinematic quantity of interest, which is a measure of the change in position per unit time. Realize how fast or variable the movement is.
• Acceleration , defined as the change in velocity per unit of time. In classical mechanics, acceleration is proportional to the net force on the particle, the constant of proportionality being its own mass.

### Types of movement

In kinematics, the types of motion are classified according to the trajectory and the value of the acceleration. In this way the following types of movement are distinguished:

1. Uniform rectilinear motion (MRU) : when the trajectory is a straight line and the acceleration is zero.
2. Uniformly Accelerated Rectilinear Motion (MRUA) : if the particle follows a straight line and the acceleration is constant and parallel to the velocity.
3. Uniformly retarded rectilinear motion (MRUR) : when the trajectory is a straight line, but the acceleration points in the opposite direction to the velocity.
4. Parabolic movement: it is a movement in the vertical plane that gives rise to a parabolic trajectory and occurs when an object is thrown into the air. Parabolic motion is the superposition of a uniform horizontal rectilinear motion and an accelerated vertical motion.
5. Uniform circular motion (MCU) : occurs when the particle moves on a circumference, describing equal arcs in equal times.
6. Uniformly Accelerated Circular Motion (MCUA) : is that which occurs when the particle moves on a circumference, such that the arc traveled increases with time following a quadratic law.

## Examples of kinematics

### Speed ​​and velocity

Speed ​​is the measure with which the position of an object changes. In loose terms, it can be said that one car goes faster than another if its position changes more in the same period of time.

Speed ​​is the quotient of the distance traveled divided by the time taken to travel that distance.

An observer on the side of the road measured the time it took for each to travel a 500m stretch and found that the yellow car took 10s, while the red car took 25s.

So the speed of the yellow car is:

500m / 10s = 50 m / s = 180 km / h

While the red car has a speed of:

500m / 25s = 20 m / s = 72 km / h

The observer is sure that the yellow car goes faster than the red one. However, to know the speed of the cars it is necessary to also know the direction of movement.

If the observer states that from left to right is the positive direction and the yellow car is going in that direction, then its speed will be +180 km / h.

But if the red car is coming from the opposite direction, then its speed will be –72 km / h.

### Instantaneous speed and average speed

When objects move they can have instantaneous variations in their speed, in fact, it is the most common situation.

For example, at a given moment the speedometer of a car reads 50 km / h, but gradually its value drops to 0 km / h because of a red traffic light. Then the light changes to green and the speedometer begins to rise to a value of 40 km / h and stays that way until the car stops again.

In a case like this, the speed is changing every moment.

If the previous route was made in a total time of 60 minutes and the total distance traveled was 20 km, then the average speed was:

20 km / 60 min = 20 km / 1 h = 20 kph.

But apart from this, the average speed does not inform about the variations that occurred in the meantime.

### Acceleration

Acceleration is the change in velocity per unit time. Speed ​​may change due to variations in:

• The speed
• The direction
• Both at the same time

Objects that fall in free fall experience acceleration, since at every moment their speed increases. The acceleration of bodies falling on the earth’s surface is approximately g = 10 m / s 2 , which means that the speed during the fall increases by 10 m / s for every second that elapses.

For example, an object that is released from rest during 2 seconds of fall acquires a speed of 20 m / s, the descent distance being 20 meters.

But if the fall occurs during 4 seconds, then it will acquire a speed of 40 m / s and the distance traveled during its descent is obviously greater: 80m.