द्रव्यमान \(m =2\) के एक कण की स्थिति, समय \(( t )\) के अनुसार \(\overrightarrow{ r }( t )=2 t \hat{ i }-3 t ^{2} \hat{ j }\) है। इस कण का मूलबिन्दु के सापेक्ष \(t =2\) पर कोणीय संवेग होगा।

\(At\,t = 2\)

\(\overrightarrow v  = 2\hat i - 12\hat j\)

\(\overrightarrow p  = m\overrightarrow v  = 4i - 24\hat j\)

\(At\,t = 2\)

\(\overrightarrow r  = 4\hat i - 12\hat j\)

\(\overrightarrow L  = \overrightarrow r  \times \overrightarrow p  = \left| \begin{array}{l}
\hat i\,\,\,\,\,\,\,\,\,\,\hat j\,\,\,\,\,\,\,\,\,\,\,\hat k\\
4\,\,\,\,\,\, - 12\,\,\,\,\,\,\,\,\,0\\
4\,\,\,\,\,\, - 24\,\,\,\,\,\,\,\,\,0
\end{array} \right|\)

\( = \left\{ {4\left( { - 24} \right) + 4 \times 12} \right\}\hat k\)

\( = \left( { - 96 + 48} \right)\hat k\)

\( = \left(  -  \right)48\,\hat k\)