3 Dynamics (AS)

3.1 Momentum and Newton's Laws of Motion:

3.1.1 Mass and resistance to change in motion:

  • Mass is the property of an object that resists changes in its motion.
  • Objects with larger mass require more force to produce a given acceleration.

3.1.2 Newton's second law of motion (F = ma):

  • The force acting on an object is equal to its mass multiplied by its acceleration.
  • The direction of acceleration and resultant force is always the same.

3.1.3 Linear momentum:

  • Linear momentum (p) is the product of an object's mass and velocity.
  • Linear momentum = mass × velocity (p = mv).

3.1.4 Force as the rate of change of momentum:

  • Force can be defined as the rate of change of momentum.
  • F = Δp/Δt (Force = change in momentum / change in time).

3.1.5 Newton's laws of motion:

  • Newton's first law (law of inertia): An object at rest or in motion will continue to remain in that state unless acted upon by an external force.
  • Newton's second law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
  • Newton's third law: For every action, there is an equal and opposite reaction.

3.1.6 Weight:

  • Weight is the force experienced by an object due to a gravitational field.
  • Weight = mass × acceleration due to gravity (W = mg).

3.2 Non-uniform motion:

3.2.1 Frictional forces and drag forces:

  • Frictional forces oppose the motion of objects in contact with each other.
  • Drag forces (including air resistance) act on objects moving through a fluid and increase with speed.

3.2.2 Motion in a uniform gravitational field with air resistance:

  • Objects in a uniform gravitational field experience a downward force (weight) and may also experience an upward force due to air resistance.
  • The interplay of these forces affects the motion of objects.

3.2.3 Terminal velocity:

  • Objects moving against a resistive force (e.g., air resistance) may reach a terminal velocity.
  • Terminal velocity is a constant velocity achieved when the resistive force equals the driving force, resulting in zero net acceleration.

3.3 Linear momentum and its conservation:

3.3.1 Conservation of momentum:

  • The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it.

3.3.2 Applications of conservation of momentum:

  • Conservation of momentum can be applied to solve problems involving interactions between objects.
  • Elastic and inelastic collisions in one or two dimensions can be analyzed using the principle of conservation of momentum.

3.3.3 Perfectly elastic collisions:

  • In a perfectly elastic collision, the relative speed of approach between objects is equal to the relative speed of separation.

3.3.4 Change in kinetic energy:

  • While momentum of a system is always conserved in interactions between objects, some change in kinetic energy may take place due to external forces or internal energy transformations.