First slide

Angular momentum

Question

A particle of mass 0.2kg is moving with linear velocity (i-j+2k). If the radius vector r = 4i+j-k, the angular momentum of the particle is

Easy

A

2.14 units
B

$\large \sqrt {4.28}$ units
C

$\large \sqrt {107}$ units
D

5 units

Solution

m = 0.2kg; $\large \bar v = \hat i - \hat j + 2\hat k,\,\bar r = 4\hat i + \hat j - \hat k\$
$\large \bar r \times \bar v = \left| {\begin{array}{*{20}{c}} {\hat i}&{\hat j}&{\hat k}\\ 4&1&{ - 1}\\ 1&{ - 1}&2 \end{array}} \right|$
$\large = \hat i\left( {2 - 1} \right) - \hat j\left( {8 - \left( { - 1} \right)} \right) + \hat k\left( { - 4 - 1} \right) = \hat i - 9\hat j - 5\hat k$
$\large \left| {\bar r \times \bar v} \right| = \sqrt {{1^2} + {{\left( { - 9} \right)}^2} + {{\left( { - 5} \right)}^2}}$
$\large = \sqrt {1 + 81 + 25} = \sqrt {107}$
$\large \left| {\bar L} \right| = m\left| {\bar r \times \bar v} \right| = 0.2\sqrt {107}$
$\large \sqrt {0.04 \times 107} = \sqrt {4.28} units$

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