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


  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 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
• 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
• Uniform object's 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 graph


  Area under graph is change in velocity

  
• Velocity-time graph


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


  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
• Free fall


  Acceleration due to gravity g
• Friction/Air resistance


  Force opposing motion, converts kinetic energy to other forms
• Lift


  Upward force on object travelling in fluid, caused by change in fluid flow direction
• Terminal speed/velocity


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

  
• Newton's 1st law


  Object remains at rest or constant velocity until resultant force acts
• 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 force
• Free-body diagram


  Diagram showing all forces acting on an object
• Momentum


  Product of mass and velocity, always conserved in closed systems
• how you how each of the forces acting on the object compare with each other. In this example, all the arrows look equal therefore we know that the car is travelling at a constant velocity.