Chapter 6

Mechanical point

Kinematics in a frame of reference

FondamentalVelocity vector

In polar coordinates :

In cylindrical coordinates :

In spherical coordinates :

Cylindrical coordinates

FondamentalAcceleration vector

In polar coordinates :

In cylindrical coordinates :

ExempleCircular 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

SimulationJAVA animations by Jean-Jacques Rousseau (Université du Mans)

  • Coordinates systems : click HERE

  • Brachistochrone curve : click HERE

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Kinematics : changing the frame of reference