SPH4U Grade 12 Physics Kinematics, Dynamics, & Circular Motion Test

Grade 12 Physics – Kinematics and Dynamics Notes


Displacement: a vector form of a distance

Velocity: a change in displacement over time

  • Slope of secant from a displacement – time graph

Instantaneous Velocity: exact speed at that point in time

  • Tangent curve of a velocity – time graph


Calculating Vectors


Vectors: a unit with magnitude and direction

  • They are resultant to vertical and horizontal movements
  • Calculated through trigonometry:
    • Head to Tail: when one vector connects to another
    • Head to Head: when vectors start at the same point
    • Vector Components
      • Break vectors into their X Y components.
      • Add individual X Y components, then find resultant



Earth: accelerates object towards center at 9.8 m/s2

  • Slight differences due to shape of the earth, but atmosphere has no impact

Drag: falling objects encounter some amount of air friction

  • Density of air will be factor


  • Cd: co-efficient of drag
  • P: density of air
  • A: surface area of object
  • V: speed of subject


Terminal Speed: when Fg = Fd, a = 0, Fnet = 0, so it will be at constant speed.


Field of Reference

  • The speed an object is moving at is dictated in relation from where you’re viewing it.
  • Example: A boat may be travelling 30m/s relative to the water, but only 20m/s relative to the ground because it’s influenced by the water’s 10m/s current.
    • Viewed from ground is different from viewing it from the water.

Calculating with field of Reference

  • General Formula: VAX = VAY + VYX
    • Where Y is common in both Vectors
    • Y is eliminated and leaves for AX, the final answer
    • Subtracting Vectors, Example: VAX = VAY – VXY
      • Add the subtracted vector by reversing the subscripts
        • VAX = VAY + VYX
        • Lastly, use Vector component or Cosine Law to add the vectors (magnitude and direction)



  • A net force causes objects to accelerate/decelerate
  • When forces act in opposite directions, they add to zero
    • Eg. Normal force counteract a surface, preventing items from falling through it.
    • Free body diagrams:  shows all forces acting on an object 
      • Useful when solving forces problems, should be drawn at all times


Inclined Planes

  • When blocks are placed on a plane, consider the surface parallel to the plane x.
  • And consider the plane perpendicular to the plane to by y.
  • Use vector components to break gravity and solve problem


Newton’s Laws and Pulley Problems

  • First Law: an object in motion stays in motion unless there is a force that slows it down
    • Inertia: this thing that makes stuff stay at constant speed, is a fundamental property of matter
    • Second Law: states that force can be affected by mass and acceleration
      • Force = Mass * Acceleration
      • Static Equilibrium: net force is zero and it doesn’t move
      • Dynamic Equilibrium: net is zero but it’s at constant speed
      • Third Law: for every action, there is a reaction, equal in magnitude but opposite in direction.


Circular Motion

  • Circular Motion: occurs when an object is travelling in a circular path with a fixed radius and speed.
  • Since direction is changing every moment in a circle, velocity changes, so the object will accelerate towards the center


  • r = radius
  • v = speed of object

ac = v2/r = 4(pi)2r/T2 = 4(pi)2rf2

  • f = frequency
  • T = period
  • Centripetal force: the force created by circular motion towards the center.
    • Centripetal force = mass * centripetal acceleration


Non-Inertial/Inertial frames of reference

  • Inertial: when the frame of reference is moving at constant speed and is not accelerating. Newton’s laws are obeyed.
  • Non-Inertial:when the frame of reference is under-going acceleration. Newton’s laws aren’t obeyed in this case.
    • When the frame of reference accelerates forward, net force is moved backwards because we say a fictitious force lifts it.


Centrifugal force

  • Centrifugal Force: another form of fictitious force which is created due to the existence of some other force
    • If centripetal force accelerates towards the center in circular motion, the centrifugal force will act against the object and whatever inside.