Question

What is the angular momentum \({\overrightarrow L _A}\)If \({\overrightarrow r _A} = (9, - 9,0)\)m and \(\overrightarrow p = (12,10,0)\)\(kg.m/s?\)

Short answer

The angular momentum \(\left( {\overrightarrow L } \right)\)\( = \left\langle {0,0,198} \right\rangle J \cdot s\)

Step-by-step solution

Definition of Angular Momentum.

The rotating inertia of an object or system of objects in motion about an axis that may or may not pass through the object or system is described by angular momentum..

The angular momentum \(\left( {\overrightarrow L } \right)\)is-

Given data

The radius vector \({\overrightarrow r _A} = \left\langle {9, - 9,0} \right\rangle m\)

The momentum vector is \(\overrightarrow p = \left\langle {12,10,0} \right\rangle kg \cdot m/s\)

The angle momentum \(\left( {\overrightarrow L } \right)\)is the cross product of radius vector \(\left( {{{\overrightarrow r }_A}} \right)\)and momentum vector \(\left( {\overrightarrow p } \right)\).That is,

\(\left( {\overrightarrow L } \right)\)\( = {\overrightarrow r _A} \times \overrightarrow p \)

\( = \left( {\left\langle {9, - 9,0} \right\rangle m} \right) \times \left( {\left\langle {12,10,0} \right\rangle kg \cdot m/s} \right)\)

\( = \left\langle { - 9 \cdot 0 - 010,0 \cdot 12 - 9 \cdot 0,9 \cdot 10 - \left( { - 9} \right) \cdot 12} \right\rangle \)

\( = \left\langle { - 0 - 0,0 - 0,90 + 108} \right\rangle \)

\( = \left\langle {0,0,198} \right\rangle J \cdot s\)

Hence, the angular momentum\(\left( {\overrightarrow L } \right)\)\( = \left\langle {0,0,198} \right\rangle J \cdot s\).