Fundamental concepts and principles of mechanics

Applied mechanics is the branch of science that deals with the effect of forces on bodies at rest or in motion. It is built on a few basic concepts and a few basic principles.

Fundamental concepts

• Space: the region occupied by bodies. Position is fixed by linear and angular measurements from a reference frame.
• Time: the measure of the succession of events. It is important in dynamics.
• Mass: the quantity of matter in a body. It is a measure of inertia, the resistance to change of motion.
• Force: the action of one body on another that tends to change its state of rest or motion. It is a vector with magnitude, direction and point of application.
• Particle: a body whose size is so small that it can be treated as a point with mass.
• Rigid body: a body in which the distance between any two points stays constant under load.

Fundamental principles

1. Newton's first law: a body stays at rest or in uniform straight-line motion unless a net external force acts on it.
2. Newton's second law: the acceleration of a body is proportional to the net force and acts in its direction, F = ma.
3. Newton's third law: to every action there is an equal and opposite reaction.
4. Newton's law of gravitation: two bodies attract each other with a force F = G m₁m₂/r².
5. Parallelogram law: two forces acting at a point can be replaced by one resultant, the diagonal of the parallelogram formed on them.
6. Principle of transmissibility: the effect of a force on a rigid body does not change if the force is moved along its line of action.