Mechanics

• What is the particle model and what are its assumptions?


  The particle model simplifies an object to a point where the dimensions are negligible, and the mass is concentrated at a single point.

  
  

  Assumptions:

  • Mass of the object is concentrated at a single point.
  • Rotational forces and air resistance can be ignored.
• What is the rod model and what are its assumptions?


  All dimensions but one are negligible, like a pole or beam.

  
  

  Assumptions:

  • Mass is concentrated along a line.
  • No thickness.
  • Rigid (does not bend or buckle).
• What is the lamina model and what are its assumptions?


  Object with area but negligible thickness, like a sheet of paper.

  
  

  Assumptions:

  • Mass is distributed across a flat surface.
• What is the light object model and what are its assumptions?


  Has a mass that is small compared to other masses involved, like a string or a pulley.

  
  

  Assumptions:

  • Treated as having zero mass.
  • Tension is the same at both ends of a light string.
• What is the inextensible string model and what are its assumptions?


  A string that does not stretch under load.

  
  

  Assumptions:

  • Acceleration is the same in objects connected by a taut inextensible string.
• What is the smooth surface model and what are its assumptions?


  A smooth surface is one where there is no friction between the surface and any objects on it.

  
  

  Assumptions:

  • No friction between the surface and any object on it.
• What is the uniform body model and what are its assumptions?


  Mass is distributed evenly.

  
  

  Assumptions:

  • Mass is concentrated at a single point at the geometrical centre of the body - the centre of mass.
• What is the wire model and what are its assumptions?


  A wire is a rigid thin length of metal.

  
  

  Assumptions:

  • Treated as one-dimensional.
• What is the smooth and light pulley model and what are its assumptions?


  A smooth and light pulley is one where the pulley has no mass and is frictionless.

  
  

  Assumptions:

  • Pulley has no mass.
  • Tension is the same on either side of the pulley.
• What is the bead model and what are its assumptions?


  A bead is a particle with a hole in it for threading on a wire or string.

  
  

  Assumptions:

  • Moves freely along a wire or string.
  • Tension is the same on either side of the bead.
• What is the rough surface model and what are its assumptions?


  A surface that is not smooth.

  
  

  Assumptions:

  • Objects in contact with the surface experience a frictional force if they are moving or are acted on by a force.
• What is the peg model and what are its assumptions?


  A support from which a body can be suspended or rested.

  
  

  Assumptions:

  • Dimensionless and fixed.
  • Can be rough or smooth as specified in question.
• What is the air resistance model and what are its assumptions?


  Air resistance is the resistance experienced on an object moves through the air.

  
  

  Assumptions:

  • Usually modelled as being negligible.
• What is the gravity model and what are its assumptions? 


  The force of attraction between all objects with mass. Acceleration due to gravity is denoted by 𝐠.

  
  

  Assumptions:

  • All objects with mass are attracted towards the Earth.
  • Earth's gravity is uniform and acts vertically downwards.
  • 𝐠 is constant and is taken as 9.8 ms⁻², unless otherwise stated in the question.