91Ó°ÊÓ

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.

Position of an object to point \(A\) is \({\overrightarrow r _A} = \left\langle {6,6,0} \right\rangle m\)

Here\(x - \) component of the position of the object, \({r_x} = 6\)

\(y - \)component of the position of the object, \({r_y} = 6\)

\(z - \)component of the position of the object,\({r_z} = 0\)

Momentum of the object relative to the point \(A\),\({\overrightarrow p _A} = \left\langle { - 11,13,0} \right\rangle kg \cdot m/s\)

Here\(x - \) component of the momentum of the object, \({p_x} = - 11\)

\(y - \)component of the momentum of the object, \({p_y} = 13\)

\(z - \)component of the momentum of the object, \({p_z} = 0\)

Angular momentum of the object relative to point \(A\)is

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

\(\begin{aligned}{}{\overrightarrow L _A} &= \left( {{r_y}{p_z} - {r_z}{p_x} - {r_x}{p_z},{r_x}{p_y} - {r_y}{p_x}} \right)\\ &= \left( {0 - 0,0 - 0,\left( 6 \right)\left( {13} \right) - \left( 6 \right)\left( { - 11} \right)} \right){\rm{kg}} \cdot {\rm{m}}/{{\rm{s}}^2}\\ &= \left( {0,078 + 66} \right){\rm{kg}} \cdot {\rm{m}}/{{\rm{s}}^2}\\ &= \left( {0,1,144} \right){\rm{kg}} \cdot {\rm{m}}/{{\rm{s}}^2}\end{aligned}\)

Hence, the Angular momentum of the object about point \(A\)is\(\left( {0,1,144} \right){\rm{kg}} \cdot {\rm{m}}/{{\rm{s}}^2}\).