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.

A rigid body is in mechanical equilibrium when the sum of the forces, and torque, experienced by the system is zero.
Equilibria can be stable or unstable:

• Stable equilibrium: The response to a small perturbation in forces and torque that tends to restore the equilibrium.

• Unstable equilibrium: The response to a small perturbation in forces and torque that tends to move the system even farther away from its original point of equilibrium (actually, the system often returns to a new stable equilibrium after the disturbance!).

This animation permits the illustration of the forces involved. The position of the center of gravity (or center of mass) of the system, in relation to its support (balancing point) is the important element  here.

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.

A balance is used to measure the mass of an object. This animation is a game where the player is asked to find the weight of an object.

Before beginning an analysis of net forces in order to study  the motion or the equilibrium of a system, one must first define…the system. Only forces exterior to the system are to be considered thereafter.
Note also that for systems at rest, or for those in uniform linear motion, the fundamental principle of dynamics (Newton’s First Law) states that the sum of the exterior forces acting on the system must be zero.

This animation enables you to compare the properties of a fixed pulley with those of a pulley system. One pulley enables you to change the direction in which a force acts. Associated  with one or several other pulleys (compound devices) the pulley enables one to reduce the force needed to lift a mass.

Note that the distance the mass is displaced is reduced by a factor identical to the factor of reduction of the force.  Thus, for a system with two pulleys, the force needed is halved, but the so is the height of displacement.  Energy is thus conserved.

Note: The friction and weight of the cord and the fasteners is ignored.

Newton's Third law of motion states that:
"For every action there is always an opposite and equal reaction". To enable the rocket to lift off , the action (thrust) from the engine must be greater than the weight of the rocket. The same condition applies to the balloon or Yosemite Sam (Copyright Warner Bros).

Hot air balloons, dirigibles and zeppelins use the principle of buoyant force discovered by Archimedes.
They are classified as being “lighter than air”, but it is important to remember that it is not the weight, but the density (weight per unit volume) that is important.
Note that this force, often neglected in accounts of forces, is omnipresent.

In your opinion, how would a Helium balloon behave on the moon?

Archimede's principle: an object immersed in fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.
You can choose between water or alcohol for the testing liquid. Materials that are less dense than the testing liquid will float.
The density of (fresh) water is 1.0 grams per cubic centimeter (g/cm3) and alcohol is about 0.8 g/cm3.
If you consider the following densities:

• ice is 0.9 g/cm3
• walnut is 0.5 g/cm3
• stone is 2 g/cm3

then you will be able to explain why the ice cube floats in water and sink in alcohol.

Safety precaution: alcohol is a flammable liquid; keep away from all flames.