**Physics Notes - Herong's Tutorial Notes** - v3.24, by Herong Yang

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

Introduction of Frame of Reference

Introduction of Special Relativity

Time Dilation in Special Relativity

Length Contraction in Special Relativity

The Relativity of Simultaneity

Minkowski Spacetime and Diagrams

Hamiltonian on Free Fall Motion

Hamiltonian on Simple Harmonic Motion

Hamiltonian on Simple Pendulum Motion

Relation of Momentum and Hamiltonian

Hamiltonian in Cartesian Coordinates

Relation of Momentum and Potential Energy

Hamilton Equations in Cartesian Coordinates

Introduction of Generalized Coordinates