A-level Mathematics/Edexcel/Mechanics 1/Mathematical Models in Mechanics

Mathematical modelling is the process of translating a real world problem into the language of mathematics, allowing the problem to be solved and a solution produced. The more accurate the model can result in a more accurate solution. Terminology This terminology is used in modelling: Particle A body whose dimensions are so small compared with other lengths involved, it can be represented as a single point. Bead A particle with a hole through the centre, allowing it to be threaded onto a string. Lamina A flat object whose thickness is small, compared with its length and breadth. In a uniform lamina equal areas have equal masses. Rigid body An object made of particles which stay in the same position, relative to each other, regardless of the forces acting on it. Rod An object that only has length, and all its mass acts along a line. In a uniform rod equal lengths have equal masses. In a non-uniform rod, equal lengths do not have equal masses. Light object An object that is assumed to have no mass. Inextensible String A string that has a constant length regardless of the forces acting on it. Smooth surface A surface that has no frictional forces. Peg A support from which a body may hang or rest.