Chapter 8

• Particle - Dimensions of the object are negligible.

  Assumptions:

  • mass of the object is concentrated at a single point
  • rotational forces and air resistance can be ignored
• Rod - All dimensions but one are negligible, like a pole or a beam.

  Assumptions:

  • mass is concentrated along a line
  • no thickness
  • rigid (does not bend or buckle)
• Lamina - Object with area but negligible thickness, like a sheet of paper.

  Assumptions:

  • mass is distributed across a flat surface
• Uniform body - Mass is distributed evenly.

  Assumptions:

  • mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass
• Light object - Mass of the object is small compared to other masses, like a string or a pulley.

  Assumptions:

  • treat object as having zero mass
  • tension the same at both ends of a light string
• Inextensible string - A string that does not stretch under load.

  Assumptions:

  • acceleration is the same in objects connected by a taut inextensible string
• Smooth surface

  Assumptions:

  • assume that there is no friction between the surface and any objects on it
• Rough surface - If a surface is not smooth, it is rough.

  Assumptions:

  • objects in contact with the surface experience a frictional force if they are moving or are acted on by a force
• Wire - Rigid thin length of metal.

  Assumptions:

  • treated as one-dimensional
• Smooth and light pulley - all pulleys you consider will be smooth and light.

  Assumptions:

  • pulley has no mass
  • tension is the same on either side of the pulley
• Bead - 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
• Peg - A support from which a body can be suspended or rested.

  Assumptions:

  • dimensionless or fixed
  • can be rough or smooth as specified in question
• Air resistance - Resistance experienced as an object moves through the air.

  Assumptions:

  • usually modelled as being negligible
• Gravity - Force of attraction between all objects. Acceleration due to gravity is denoted by g.

  Assumptions:

  • assume that 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 9.8m/s^-2, unless otherwise stated in the question
• The International System of Units (SI) is the modern form of the metric system. These base units are most commonly used in mechanics:

  • mass - kilograms, kg
  • length/displacement - metre, m
  • time - seconds, s

  These derived units are compound units built from the base units:

  • speed/velocity - metres per second, m/s^-1
  • acceleration - metres per second per second, m/s^-2
  • weight/force - newton, N
• The weight of an object acts vertically downwards.
• The normal reaction is the force which acts perpendicular to a surface when an object is in contact with the surface.
• The friction is a force which opposes the motion between two rough surfaces.
• If an object is being pulled along by a string, the force acting on the object is called the tension in the string.
• If an object is being pushed along using a light rod, the force acting on the object is called the thrust or compression in the rod.
• Buoyancy is the upward force on a body that allows it to float or rise when submerged in a liquid.
• Air resistance opposes motion.
• A vector is a quantity which has both magnitude and direction.
• Displacement is the distance in a particular direction (metre-m)
• Velocity is the rate of change of displacement (metres per second-m/s^-1)
• Acceleration is the rate of change of velocity (metres per second per second-m/s^-2).
• Force/weight is described by magnitude, direction and point of application (newton-N)
• A scalar quantity has magnitude only.
• Distance is the measure of length (metre-m)
• Speed is the measure of how quickly a body moves (metres per second-m/s^-1)
• Time is a measure of ongoing events taking place (second-s)
• Mass is a measure of the quantity of matter contained in an object (kilogram-kg)
• Scalar quantities are always positive. When considering motion in a straight line, vector quantities can be positive or negative.
• Distance is the magnitude of the displacement vector.
• Speed is the magnitude of the velocity vector.