Newton's Laws Notes

Newton's Laws

Objectives

  • Apply Newton’s second law to the motion of a particle in two dimensions.
  • Derive the equation of motion of a projectile in a vacuum.

Part 1: Revision

  • Force Definition: A mechanical action exerted by one object on another (push or pull).
  • Force Characteristics:
    • Point of application
    • Direction
    • Sense
    • Magnitude (Newtons, N)
  • Examples of Forces:
    • Weight
    • Tension of a string
    • Normal reaction of a support
    • Friction
  • Weight (\W):
    • Exerted by Earth.
    • Point of application: Center of gravity “G”.
    • Direction: Vertical.
    • Sense: Downwards.
    • Magnitude: W=m×gW = m \times g
  • Tension (\T):
    • Exerted by a string.
    • Point of application: Contact point.
    • Direction: Along the string.
    • Sense: Towards the string.
    • Magnitude: T=K⋅xT = K \cdot x (K: stiffness, x: extension)
  • Normal Reaction (N\N):
    • Exerted by a rigid surface.
    • Point of application: Middle of contact surface.
    • Direction: Perpendicular to the surface.
    • Sense: Away from the surface.
  • Friction Force (\f):
    • Exerted by a rough surface.
    • Point of application: Middle of the contact surface.
    • Direction: Along the surface.
    • Sense: Opposite to the direction of motion.
  • Free Body Diagram: Illustration of all external forces acting on a single point representing the body.
    *Note: Internal forces don't affect the motion.
  • Force Projection:
    • Along x-axis: F<em>x=Fcos⁡θF<em>x = F \cos\theta *Along y-axis: F</em>y=Fsin⁡θF</em>y = F \sin\theta
  • Net Force: The sum of all external forces: F⃗net=N⃗+W⃗+f⃗\vec{F}_{net} = \vec{N} + \vec{W} + \vec{f}

Part 2: Newton’s Laws

  • Mechanics:
    • Dynamics: Motion under forces.
    • Kinematics: Motion without reference to forces.
    • Statics: Equilibrium under forces.
  • Newton’s First Law (Law of Inertia): If F⃗ext=0\vec{F}_{ext} = 0, the body is in equilibrium (at rest or constant speed).
  • Inertia: Tendency to remain at rest or in motion; related to mass.
  • Newton’s Second Law: F⃗ext=ma⃗\vec{F}_{ext} = m\vec{a} (Acceleration is proportional to net force and inversely proportional to mass).
  • The acceleration is in the same sense as the net force.