When a force tends to make an object turn on an axis (around a pivot point) one can define the moment (or torque) of this force in relation to the pivot point.

In Mechanics , the study of the moment of a rotating body is the equivalent of the study of forces for bodies undergoing translation.

The vector moment is a function of the force and the distance seperating the pivot point of the axis from that force  (called the lever arm or moment arm – not shown in the animation).  The mathematical formula that enables us to determine the moment (torque) brings into play the operator vector product (note “X”).

The particularity of the resulting vector moment is that its direction is perpendicular to vectors F and OM (or OQ). Its module depends on the sine of the angle between F and OM. Its strength is thus maximal for an angle of 90° and zero when the direction of the force passes along the axis.

The term couple is associated with a system of two forces where the resultant is zero (one pushes while the other pulls) but where the moment is not zero. In this example, one can speak of a couple if one force F’ of the same amplitude but opposite in direction, was applied to the other pedal.

Animation brought to you in cooperation with the Musée des Arts et Métiers - Paris.

The velocipede (literally "fast foot") uses a chain set with a fixed sprocket on the front wheel: one turn of the pedals is the equivalent of one turn of the driving wheel.

To travel greater distances with each turn of the pedals it is necessary to increase the diameter of the front wheel: the Penny Farthing is an extreme application of this principle.

The bicycle uses a transmission system that involves a chain connecting two sprockets of different sizes, which provides greater distance to be covered with each turn of the pedals.

Animation brought to you in cooperation with the Musée des Arts et Métiers - Paris.

The velocipede (literally "fast foot") uses a chain set with a fixed sprocket on the front wheel: one turn of the pedals is the equivalent of one turn of the driving wheel.

To travel greater distances with each turn of the pedals it is necessary to increase the diameter of the front wheel: the Penny Farthing is an extreme application of this principle.

The bicycle uses a transmission system that involves a chain connecting two sprockets of different sizes, which provides greater distance to be covered with each turn of the pedals.

A gear system enables the transmission of motion. In this example, which deals exclusively  with toothed wheels, only rotational motion is dealt with.  The speeds of rotation are a function of the gear ratio (or transmission ratio), which depends solely on the number of teeth on each wheel.

Knowing that the number of teeth is proportional to the wheel's diameter, we can also define the gear ratio as a function of wheel diameters.

A gear system ensures  a transmission without slippage, and with a very high yield. The gear ratio can be greater than 1 (muliplication) or less than 1 (reduction).  Augmentation of the couple  produces a decreased speed, and vice versa.

Sometimes, an object moves within a medium which is moving with respect to a fixed observer. Here you have a boat sailing straight right. in a current. Therefore the magnitude of the velocity of the boat with respect to a fixed observer on land will not be the one indicated by the speedometer on-board.
This simulation is an application of the velocity composition law:

• The green vector is the velocity of the boat relative to the ground.
• The red vector is the velocity of the boat relative to the water.
  
• The blue vector is the velocity of the water relative to the ground.

The velocity of the boat relative to the ground (the only one necessary to determine the sailing route) is the addition of the two others.
These considerations would be the same for an airplane which encounters a wind.

Kinematics is the branch of Mechanics that studies the motion of bodies. To better apprehend the movement of a body, the physicist studies the evolution over time of the following three quantities:

    1. Position
    2. Speed
    3. Acceleration

Changes over time are here traced in the form of a graph. You will find here graphs for uniform linear motion at constant speed and under conditions of a constant acceleration.
The study of the forces applied to the car shows that the sum of these forces is zero for constant speed, but not for the case of uniform acceleration.

Angular velocity is the rate of change of angular displacement. The protractor will help you to introduce the different units commonly used: Hz, Rad/s, rpm ...

Example of translation along a circular path. Do not confuse this with rotational transformation.