mechanics AS

• 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, velocity = displacement / time
• Center of mass


  • For uniform shapes, the center of mass always acts at the center
  • If the center of mass is within the base, the object is quite stable
• Center of gravity


  • Where the weight force is acting
• If the 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
• Displacement-time graph


  1. Gradient = velocity

  2. Positive and negative displacement

  3. Gradient can change
• Velocity-time graph


  1. Gradient = acceleration

  2. Positive and negative velocity

  3. Constant, increasing, decreasing acceleration
• Acceleration-time graph


  1. Positive and negative acceleration

  2. Constant acceleration

  3. Deceleration
• Average velocity


  (Initial velocity + Final velocity) / 2
• The SUVAT equations allow finding the unknown variable if 3 are known
• Projectile motion


  Motion with no horizontal acceleration, parabolic path
• Upwards is positive direction, downwards is negative for projectile motion
• Acceleration due to gravity (g) is 9.81 m/s^2
• Terminal speed


  Speed at which the drag force equals the weight force, no further acceleration
• Newton's Laws


  • No net force, object remains at constant velocity
  • Net force is proportional to rate of change of momentum
  • Forces between objects are equal and opposite
• Momentum


  Mass x Velocity, a vector quantity
• Momentum is conserved in explosions and collisions
• We have to talk about an event, either an explosion where initially things were both at rest and they move away in different directions, or a collision where things come together and then they might stick together or move off again in different directions
• Object 1


  Mass m1, initial velocity u1
• Object 2


  Mass m2, initial velocity u2
• The momentum before is equal to m1*u1 + m2*u2
• After the event, the objects might move off in the same direction, different directions, or stick together
• The total momentum before and after is conserved, provided linear momentum is conserved