Angular Momentum Of A Particle

The angular momentum of a single particle about a point is $L=mv{r}_{\perp }$, where $r_{\perp }$ is the perpendicular distance from the point to the line of motion. A key conceptual point is that even straight-line motion carries nonzero angular momentum about a point lying off its path. Substituting the given data, $L=(0.5)(4)(3)=6{\text{ kg m}}^2/\text{s}$. The value 2 kg m${}^2$/s uses only $mv$ and forgets the perpendicular distance. The value 12 kg m${}^2$/s drops the mass factor of 0.5 and effectively doubles the result. The value 24 kg m${}^2$/s omits the mass entirely and mishandles the remaining product. This is the NCERT definition $\vec{L}=\vec{r}\times \vec{p}$, here reduced to its magnitude because the line keeps a fixed perpendicular distance of 3 m. As a dimensional check, kilograms times metres per second times metres gives kg m${}^2$/s, the correct unit of angular momentum, and the modest input values yield a sensible 6 kg m${}^2$/s.