Physics Notes - Herong's Tutorial Notes

∟Introduction of Hamiltonian

∟What Is Momentum

This section provides a quick introduction of momentum defined as the product of the mass and the velocity of a moving object.

What Is Momentum? Momentum is a physical quantity, p, of a moving object defined as the product of the mass, m, and the velocity, v, of the object: 

p = m*v                            (H.7)
  # p is the momentum
  # m is the mass
  # v is the velocity

Momentum is related to the force through Newton's Second Law which states that the rate of change of the momentum of an object is equal to the force, F, acting on the object: 

F = dp/dt                          (H.8)

or:
  F = p'                           (H.8)
    # p' is the derivative of momentum against time

If we assume mass is a constant, H.8 becomes the common form of Newton's Second Law: 

F = dp/dt                          (H.8)

or:
  F = d(m*v)/dt
  F = m*dv/dt
  F = m*a                          (H.5)
    # a is the acceleration

Table of Contents

 About This Book

 Introduction of Space

 Introduction of Frame of Reference

 Introduction of Time

 Introduction of Speed

 Newton's Laws of Motion

 Introduction of Special Relativity

 Time Dilation in Special Relativity

 Length Contraction in Special Relativity

 The Relativity of Simultaneity

 Introduction of Spacetime

 Minkowski Spacetime and Diagrams

►Introduction of Hamiltonian

 What Is Hamiltonian

 Hamiltonian on Free Fall Motion

 Hamiltonian on Simple Harmonic Motion

 Hamiltonian on Simple Pendulum Motion

►What Is Momentum

 Relation of Momentum and Hamiltonian

 Hamiltonian in Cartesian Coordinates

 Relation of Momentum and Potential Energy

 Hamilton Equations in Cartesian Coordinates

 Introduction of Lagrangian

 Introduction of Generalized Coordinates

 Phase Space and Phase Portrait

 References

 Full Version in PDF/ePUB