First slide

Angular momentum

Question

If the velocity of a rotating body of mass 50 kg is given by $\large \vec V = 3\vec {\,i\,} + 4\vec {\,j\,} + 5\vec{\,k\,}$ and radius vector $\large \vec r = 2\vec {\,i\,} + 3\vec {\,j\,} + 4\vec{\,k\,}$ , then its angular momentum is.

Moderate

A

$\large 50\vec {\,i\,} + 50\vec {\,j\,} + 50\vec{\,k\,}$
B

$\large 50\vec {\,i\,} + 100\vec {\,j\,} + 50\vec{\,k\,}$
C

$\large 50\vec {\,i\,} + 50\vec {\,j\,} + 100\vec{\,k\,}$
D

$\large -50\vec {\,i\,} + 100\vec {\,j\,} - 50\vec{\,k\,}$

Solution

$\large \vec r \times \vec v = \left| {\begin{array}{*{20}{c}} {\hat i}&{\hat j}&{\hat k}\\ 2&3&4\\ 3&4&5 \end{array}} \right|$
$\large = \hat i\left( {15 - 16} \right) - \hat j\left( {10 - 12} \right) + \hat k\left( {8 - 9} \right) = - \hat i + 2\hat j - \hat k$
$\large \vec L = m\left( {\vec r \times \vec v} \right) = 50\left( { - \hat i + 2\hat j - \hat k} \right)$
$\large = - 50\,\hat i + 100\hat j - 50\hat k$

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