Chapter 6

# Kinematics in a frame of reference

## Fondamental : Velocity vector

In polar coordinates :

In cylindrical coordinates :

In spherical coordinates :

Cylindrical coordinates

## Fondamental : Acceleration vector

In polar coordinates :

In cylindrical coordinates :

## Exemple : Circular motion

Let be the radius of a circle.

The angular velocity vector is :

Where is the usual angle of polar coordinates.

Circular motion

The velocity vector is :

The acceleration vector is :

If we consider a uniform motion ( ) :

The acceleration is purely centripetal.

A few exemples of motions of a material point :

A few exemples of motions of a material point