Newton’s Second Law of Motion

Newton’s second law of motion states that there exists frames of reference in which the motion of the particle is described by the differential equation

\[\begin{equation} \textbf{F} = \frac{d\textbf{p}}{dt} = \dot{\textbf{p}} \end{equation}\]

Or,

\[\begin{equation} \textbf{F} = \frac{d}{dt} \left(m\textbf{v}\right) \end{equation}\]

Definition of angular momentum

The angular momentum of the particle about point O, denoted by L, is defined as

\[\begin{equation} \textbf{L} = \textbf{r} \times {\textbf{p}} \end{equation}\]

Definition of Moment of force

The moment of force or torque about O, denoted by N, is defined as

\[\begin{equation} \textbf{N} = \textbf{r} \times {\textbf{F}} \end{equation}\]

Taking the cross product with r the equation of F, we can show that

\[\begin{equation} \textbf{N} = \dot{\textbf{L}} \end{equation}\]

where, both L and N depend on the point O about which the moments are taken.

The conservation theorem for linear and angular momentum of a particle follows from respective equations above.

TODO: Add something about Energy Conservation Theorem for a particle

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Last Updated: Thursday, 2nd Jan, 2020, 23:13 NPT Author: Madhav Humagain (scimad)