In part a of the figure, particles 1 and 2 move around point O in opposite directions, in circles with radii 2 m and 4 m. In part b, particles 3 and 4 travel in the same direction along straight lines at perpendicular distances of 4 m and 2 m from point O. Particle 5 moves directly away from O. All five particles have the same mass and the same constant speed.

Rank the particles according to the magnitudes of their angular momentum about point O, greatest first.

Which particles have negative angular momentum about point O?

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Angular momertum \vec{L}=m(\vec{r} \times \vec{v})for particle-1, \vec{L}_{1}=m(\vec{r} \times \vec{v})=m v r_{1} \hat{k}r_{1}=4 m, \quad \vec{L}_{1}=4 m v(-\hat{k})Particle-2, \vec{L}_{2}=m\left(\vec{r}_{2} \times \vec{v}\right)=m v r_{2}(-\hat{k})r_{2}=2 m, \quad \vec{L}_{2}=2 m v(-\hat{k})Particle-3\begin{array}{ll}\text { Particle-3, } & \vec{L}_{3}=m\left(\vec{r}_{3} \times v\right)=\operatorname{mvr_{3}}(-\hat{k}) \\& \vec{L}_{3}=-4 m v(\hat{k}) \\\text { Particle-4 } & \overrightarrow{L_{4}}=m\left(\vec{r}_{4} \times \vec{v}\right)=\operatorname{mvr}_{4}(\hat{k}) \\& \vec{L}_{4}=2 m v(\hat{k}) \\\text { Partile }-(5) & \vec{L}_{5}=m\left(\vec{r}_{5} \times \vec{v}\right)=0\end{array}Part-(9) Rank as per maynitudeL_{1}=L_{3}=L_{2}=L_{4}>L_{5}Part-(b) Negative angular momentumParticle \rightarrow 2 & 3 ...