A rigid body consists of a 3 kg mass and a 2 | vedclass

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(B) The length of the rod is the distance between the two masses: $L = |\vec{r}_2 - \vec{r}_1| = \sqrt{(4 - 2)^2 + (2 - 5)^2} = \sqrt{2^2 + (-3)^2} =

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$\sqrt{13} \ m, \left( \frac{14}{5} \hat{i} + \frac{19}{5} \hat{j} \right) \ m$

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(B) The length of the rod is the distance between the two masses: $L = |\vec{r}_2 - \vec{r}_1| = \sqrt{(4 - 2)^2 + (2 - 5)^2} = \sqrt{2^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13} \ m$. The center of mass $\vec{r}_{CM}$ is given by: $\vec{r}_{CM} = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2}{m_1 + m_2} = \frac{3(2 \hat{i} + 5 \hat{j}) + 2(4 \hat{i} + 2 \hat{j})}{3 + 2}$ $\vec{r}_{CM} = \frac{(6 \hat{i} + 15 \hat{j}) + (8 \hat{i} + 4 \hat{j})}{5} = \frac{14 \hat{i} + 19 \hat{j}}{5} = \left( \frac{14}{5} \hat{i} + \frac{19}{5} \hat{j} \right) \ m$.

$A$ rigid body consists of a $3 \ kg$ mass and a $2 \ kg$ mass connected by a massless rod. The $3 \ kg$ mass is at $\vec{r}_1 = (2 \hat{i} + 5 \hat{j}) \ m$ and the $2 \ kg$ mass is at $\vec{r}_2 = (4 \hat{i} + 2 \hat{j}) \ m$. Find the length of the rod and the coordinates of the center of mass.

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