## Kinematics theory

# Kinematics

Kinematics is the branch of classical mechanics that describes the motion of bodies (objects) and systems (groups of objects) without consideration of the forces that cause the motion.

When we study the motion of a body, we always have to do it respect to a Reference System, which is a point or set of points through which we describe the movement that a body has.

We say that a body is moving respect to a Reference System when it changes its position over the time, if it doesn’t change, we will say that it is in repose. The movement is relative, that is, it will depend on the reference system we choose.

If we join all the points where passes a body, we obtain a curve called **trajectory**, on which we can determine the position of a point that after join it with OX and OY axes, we obtain as result a vector called **position vector**.

The length or module of that position vector is calculated by:

**FORMULA SUMMARY:**

Scalar average velocity

Scalar instant velocity

Vectorial average velocity

Vectorial instant velocity

Average acceleration

Instant acceleration

Tangential acceleration

Normal acceleration

Rectilinear uniform motion

Rectilinear uniformly varied motion

Free fall motion

Angular magnitudes

Angular velocity

Angular acceleration

Uniform circular motion (T = period ; f = frequency)

Uniform circular varied motion

Vibratory harmonic motion (s = elongation ; A = amplitude ; ω = pulsation)

**COMPOSITION OF MOVEMENTS**

Vertical launch of projectiles

Horizontal launch of projectiles

Oblique launch of projectiles

Trajectory equation

Maximum Height

Final scope

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