Mechanics and Materials

• Scalars


  Physical quantities that describe only a magnitude
• Vectors


  Physical quantities that describe magnitude and direction
• Examples of scalars


  • Distance, speed, mass, temperature
• Examples of vectors


  • Displacement, velocity, force/weight, acceleration
• Adding vectors - Calculation

  1. Use Pythagoras to find resultant magnitude

  2. Use trigonometry to find direction
• Adding vectors - Scale drawing

  1. Draw scale diagram using ruler and protractor

  2. Measure magnitude and direction from diagram
• Resolving vectors


  Splitting a vector into perpendicular components using trigonometry

  
• Formulas for resolving vectors: x = V cos θ, y = V sin θ
• Hint for resolving vectors: Use cos for components in the direction of the angle, use sin for components perpendicular to the angle
• Equilibrium


  When the sum of all forces acting on an object is zero, so it is either at rest or moving at constant velocity
• Showing equilibrium


  1. Add horizontal and vertical components of forces, showing they equal zero

  2. Draw scale diagram, if it forms a closed triangle then object is in equilibrium
• Moment of a force


  Force multiplied by perpendicular distance from line of action of force to point
• Couple


  Pair of coplanar forces equal in magnitude but acting in opposite directions
• Moment of a couple


  One of the forces multiplied by perpendicular distance between lines of action of forces
• Principle of moments


  For an object in equilibrium, sum of anticlockwise moments = sum of clockwise moments
• Centre of mass


  Point at which an object's mass acts
• If an object is uniform, its centre of mass is at its centre
• Speed


  Scalar quantity describing how quickly an object is travelling
• Displacement


  Vector quantity describing the overall distance travelled from starting position
• Velocity


  Rate of change of displacement
• Acceleration


  Rate of change of velocity
• Instantaneous velocity


  Velocity at a specific point in time, found from gradient of displacement-time graph
• Average velocity


  Velocity over a specified time frame, found by dividing final displacement by time taken
• Uniform acceleration


  Acceleration is constant
• Acceleration-time graphs


  • Area under graph is change in velocity

  
• Velocity-time graphs


  • Gradient is acceleration, area under graph is displacement
• Displacement-time graphs


  • Gradient is velocity
• Formulas for uniformly accelerated motion


  • v = u + at
  • s = (u+v)t/2
  • s = ut + at^2/2
  • v^2 = u^2 + 2as
• Projectile motion


  Vertical and horizontal components are independent, can be evaluated separately using uniform acceleration formulas
• Free fall


  Motion with constant acceleration of g (9.81 m/s^2)
• Friction


  Force opposing motion, converts kinetic energy to other forms
• Air resistance


  Frictional force experienced by objects moving through fluid, increases with speed
• Lift


  Upward force on objects moving through fluid, caused by change in fluid flow direction
• Terminal speed


  Speed at which frictional forces equal driving forces, so no acceleration
• Air resistance affects both vertical and horizontal components of projectile motion

  
• Newton's 1st law


  An object will remain at rest or travelling at constant velocity until a resultant force acts on it
• Newton's 2nd law

  Acceleration is proportional to resultant force, F = ma
• Newton's 3rd law


  For every force, there is an equal and opposite reaction force
• Free-body diagram


  Diagram showing all forces acting on an object
• Momentum


  Product of mass and velocity, always conserved in closed systems