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  4. A particle has the position vector r = hati - 2 hatj + hatk and the linear momentum p = 2 hati - hatj + hatk. Its angular momentum about the origin is

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Q. A particle has the position vector ${r} = \hat{i} - 2\hat{j } + \hat{k}$ and the linear momentum ${p} = 2\hat{i} - \hat{j} + \hat{k}$. Its angular momentum about the origin is

KEAMKEAM 2014System of Particles and Rotational Motion

Solution:

Given,
$r =\hat{ i }-2 \hat{ j }+\hat{ k } $
$p =2 \hat{ i }-\hat{ j }+\hat{ k }$
Angular momentum
$J = r \times p$
$=(\hat{ i }-2 \hat{ j }+\hat{ k }) \times(2 \hat{ i }-\hat{ j }+\hat{ k })$
$J =\begin{vmatrix}\hat{ i } & \hat{ j } & \hat{ k } \\ 1 & -2 & 1 \\ 2 & -1 & 1\end{vmatrix}$
$J =\hat{ i }(-2+1)-\hat{ j }(1-2)+\hat{ k }(-1+4)$
$J =-\hat{ i }+\hat{ j }+3 \hat{ k }$