Mechanics

• Particle

  • Mass of the object is concentrated at a single point
  • Rotational forces and air resistance can be ignored
• Rod

  • Mass is concentrated along a line
  • No thickness
  • Rigid (does not bend)
• Lamina

  • Mass is distributed across a flat surface
• Uniform body

  • Mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass
• Light object

  • Treat object as having zero mass
  • Tension the same at both ends of a light string
• Inextensible string

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

  • Assume that there is no friction between the surface and any object on it
• Rough surface

  • Objects in contact with the surface experience a frictional force if they are moving or are acted on by a force
• Wire

  • Treated as one-dimensional
• Smooth and light pulley

  • Pulley has no mass
  • Tension is the same on either side of the pulley
• Bead

  • Moves freely along a wire of string
  • Tension is the same on either side of the bead
• Peg

  • Dimensionless and fixed
  • Can be rough or smooth as specified in question
• Air resistance

  • Usually modelled as being negligible
• Gravity

  • Assume that all objects with mass are attracted towards the earth
  • Earths gravity is uniform and acts vertically downwards
  • g is constant and is taken as 9.8ms-2, unless otherwise stated in the question
• The weight (or gravitational force) 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 c 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. (E.g. the weight of a parachutist acts vertically downwards and the air resistance acts vertically upwards)
• A vector is a quantity which has both magnitude and direction (E.g. displacement, velocity, acceleratio, force/weight)
• A scalar quantity has magnitude only. (E.g. distance, speed, time, mass)
• Scalar quantities are always positive while vector quantities can be positive or negative.
• Velocity is that rate of change of displacement.

  • On a displacement time graph the gradient represents the velocity
  • If the displacement time graph is a straight line, then the velocity is constant
• Average velocity = displacement from starting point/time taken.
• Acceleration is the rate of change of velocity

  • In a velocity time graph the gradient represents the acceleration
  • If the velocity time graph is a straight line, then the acceleration is constant
• The area under the velocity time graph represents the distance travelled.
• SUVAT

  S is the displacement

  U is the initial velocity

  V is the final velocity

  A is the acceleration

  T is the time
• SUVAT formula

  v=u+at

  s=(u+v/2)t

  v^2=u^2+2as

  s=ut+1/2at^2

  s=vt-1/2at^2
• Newton‘s first law of motion states that an object at rest will stay at rest and that an object moving with constant velocity will continue to move with constant velocity unless an unbalanced force acts on the object.
• A resultant force acting on an object will cause the object to accelerate in the same direction as the resultant force.
• Newton’s second law of motion states that the force needed to accelerate a particle is equal to the product of the mass of the particle and the acceleration produced: F=ma.
• Newton’a third law states that for every action there is an equal and opposite reaction.