A level math Mechanic 2

1. Motion of a projectile

• Introduction
• Particle projected at an upward angle from a height above ground
• Particle projected at a downward angle from a height above ground
• Particle projected horizontally from a height
• Finding the speed and direction at a given time
• derive and use the cartesian equations of the trajectory of a projectile,
  including problems in which the initial speed and/or angle of projection
  may be unknown. (still to be done)
• Exam Questions

2. Equilibrium of a rigid body

Moments

• What is the moment of a force?
• Horizontal rods / planks / beams in equilibrium resting on :

• one support
• two supports
• Tilting
  • Tilting example
• Exam Questions (1)

• Forces at an Angle
  • Moment of a non-perpendicular force
• Ladder type problems
  • Ladder leaning against a smooth wall and floor
  • Ladder leaning against a smooth wall but on a rough floor
• Exam Questions (2)

Centre of Mass

• Particles
  • Centre of mass of a system of particles in a line
  • Centre of mass of a system of particles in a plane
• Uniform Laminas
  • Centre of mass of a uniform lamina that has lines of symmetry
  • Triangular laminas
  • Sectors and semi-circles
• Composite Laminas
  • rectangles
  • rectangle + triangle
  • rectangle + semi-circle
  • rectangle with circle removed
• Wire Frameworks
  • Wire framework consisting of a rectangle and triangle
• Hanging Problems
  • Freely suspended lamina
• Toppling Problems
  • Lamina on an inclined plane

Exam Questions

• Exam Questions

3. Uniform motion in a circle

• understand the concept of angular speed for a particle moving in a
  circle, and use the relation v = rω
• understand that the acceleration of a particle moving in a circle with
  constant speed is directed towards the centre of the circle, and use
  the formulae rω² and v²/r
• solve problems which can be modelled by the motion of a particle
  moving in a horizontal circle with constant speed

4. Hooke's law

• use Hooke’s law as a model relating the force in an elastic string or
  spring to the extension or compression, and understand the term
  modulus of elasticity;
• use the formula for the elastic potential energy stored in a string or
  spring
• solve problems involving forces due to elastic strings or springs,
  including those where considerations of work and energy are needed.

5. Linear motion under a variable force

• use dx/dt for velocity, and dv/dt or v dv/dx for acceleration, as appropriate
• solve problems which can be modelled as the linear motion of a
  particle under the action of a variable force, by setting up and solving
  an appropriate differential equation (restricted to equations in which
  the variables are separable).