mechanics

• Scalar quantities


  Quantities that only have a size or magnitude
• Vectors


  Quantities that have both a size (magnitude) and a direction
• Examples of scalar quantities


  • Distance
  • Speed
  • Mass
• Examples of vector quantities


  • Displacement
  • Velocity
  • Acceleration
  • Weight
  • Force
• Displacement


  The distance between the start and end position, including direction
• Velocity


  The rate of change of displacement
• Acceleration


  The rate of change of velocity
• Mass


  The amount of matter an object contains
• Weight


  The force exerted by gravity on an object with mass
• Adding vectors


  1. Draw scale diagram

  2. Measure angle with protractor

  3. Find resultant
• Resolving a vector


  1. Find horizontal component (F_x = F cos(θ))

  2. Find vertical component (F_y = F sin(θ))
• If an object is in equilibrium, the sum of the forces is zero and the sum of the moments is zero
• Moment of a force


  Force x perpendicular distance from point to line of action of force
• Moment of a couple

  Force x distance between parallel forces
• The principle of moments states that in equilibrium, the total clockwise moments = total anticlockwise moments
• Center of mass


  The point at which an object's mass appears to act
• If the center of mass is within the base, the object is stable
• Speed = distance / time
• Center of mass


  • Acts at the center for uniform shapes
  • If center of mass is within the base, the object is quite stable
• The center of mass of a ruler with different masses hung on it is at the midpoint
• Velocity (V)


  The rate of change of displacement (s) over time (t)
• Average velocity


  The total displacement divided by the total time
• Instantaneous velocity


  The velocity at a particular time
• Acceleration (a)


  The rate of change of velocity over time
• Displacement-time graph


  1. Gradient = velocity

  2. Positive and negative displacement possible
• Velocity-time graph


  1. Gradient = acceleration

  2. Positive and negative velocity possible

  3. Constant acceleration

  4. Deceleration
• Acceleration-time graph


  1. Positive and negative acceleration possible

  2. Constant negative acceleration (e.g. in projectile motion)
• Average velocity


  (Initial velocity + Final velocity) / 2
• The SUVAT equations allow you to find the unknown variable if you know any 3 of the 5 variables (s, u, v, a, t)
• Motion in 2D (projectile motion)


  • Horizontal and vertical motion are independent

  Acceleration in horizontal direction is 0

  Acceleration in vertical direction is -g (due to gravity)
• In reality, moving objects experience drag forces which affect their motion
• Falling objects reach a terminal speed where the drag force equals the weight force
• Newton's 1st Law


  An object at rest stays at rest, and an object in motion stays in motion, unless acted upon by an unbalanced force
• Newton's 2nd Law


  The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass
• Newton's 3rd Law


  For every action, there is an equal and opposite reaction
• Momentum (p)


  The product of an object's mass and velocity
• Momentum is conserved in closed systems (e.g. explosions, collisions)
• We have to talk about an event so this could be an explosion where initially things were both at rest and they move away in different directions or we could talk about a collision where things come together and then it might kind of stick together or they might move off again in different directions
• Object 1


  Mass m1, initial velocity u1
• Object 2


  Mass m2, initial velocity u2