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unit 3
3.1 momentum and newton's laws of motion 3.2 non-uniform motion 3.3 linear momentum and its conservation
3.1

momentum and newton’s laws of motion

relationships involving force and mass

  • forces are vector quantities — they have both magnitude and direction
  • a free-body diagram shows the forces acting on an object
  • the resultant force is the combined effect of all forces acting on an object
  • if forces are balanced, the resultant force is 0

forces and motion

  • an object remains at rest or in constant velocity unless acted upon by a resultant force
  • a resultant force is required to change velocity
  • a change in velocity means a change in speed, direction, or both

newton’s laws of motion

first law

  • an object continues in its state of rest or uniform motion unless acted upon by a resultant force
  • this is sometimes described as inertia

second law

  • acceleration is directly proportional to the resultant force
  • acceleration is inversely proportional to mass
  • acceleration is always in the same direction as the resultant force
  • F = ma

where:

  • F = resultant force (N)
  • m = mass (kg)
  • a = acceleration (m s⁻²)

third law

  • when one object exerts a force on another, the second object exerts an equal and opposite force on the first
  • these forces act on different objects
  • they are known as action–reaction pairs

momentum

  • momentum is the product of mass and velocity
  • p = mv
  • momentum is a vector quantity
  • unit: kg m s⁻¹ or N s

newton’s second law in terms of momentum

  • resultant force equals the rate of change of momentum
  • F = Δp / t
  • this is the more general form of newton’s second law

link to third law

  • the rate of change of momentum of one object is equal and opposite to that of the other object
  • this explains why action–reaction forces are equal in magnitude and opposite in direction

weight

  • weight is the force due to gravity acting on a mass
  • W = mg
  • g ≈ 9.81 m s⁻²
  • weight acts vertically downwards

when an object rests on a surface, its weight is balanced by a normal contact force.

identifying newton’s third law pairs

  • forces must act on two different objects
  • forces must be equal in magnitude
  • forces must act in opposite directions
  • forces must be of the same type

as shown in the diagram, R acts on the book, while R' acts on the surface. this means that this is a third law pair.