Force
A force F is a vector quantity, which means that it has both a magnitude and a direction associated with it. If we consider two particles characterized by mass m1 and mass m2 at a distance d from each other, an interaction between the two particles causes particle 1 to accelerate towards particle 2 and vice versa. It can be shown that m1a1 = -m2a2 where a1 and a2 represent the accelerations of particle 1 and particle 2. If we define F12 = m1a1 and F21 = m2a2 we can say that F12 = - F21, where F12 is the force acting on particle 1 due to particle 2 and F21 is the force acting on particle 2 due to particle 1 (Figure 1).
Figure 1: Interaction forces between two particles
In the SI unit system the unit of force is derived from
the equation F = ma. A force of 1 Newton, N, is defined as the force that gives an
acceleration of 1 m/s2 to a mass of 1 kg, thus 1 N = 1 kg*m/s2.
Moment
The moment of a force is a vectorial quantity. The magnitude of a moment Mp of a force F about a point p is equal to the force F times the distance L of the line of application of the force from point p:
Figure 2: Moment of a force
A torque produces a rotation in the same way a force produces a translation. An example of moment of a force is shown in Figure 2. If we imagine to push a door by applying a force of magnitude F as shown above, the moment Mp produces an angular acceleration of the door about pivot p, causing the door to rotate counter-clock-wise. Moment as a vector is perpendicular to the plane of rotation and it points in the direction of the observer who sees a counter clock wise rotation (in the above example the moment points out of the screen). In the SI unit system the unit of force is N*m.
