Intro to Center of Mass Video Lessons

Concept

# Problem: A. Find the coordinates of the center of mass. Find the x-coordinate. Find the y-coordinate.B. Find the moment of inertia about a diagonal axis that passes through masses B and D.

###### FREE Expert Solution

X-coordinate of the center of mass:

$\overline{){{\mathbf{x}}}_{\mathbf{c}\mathbf{m}}{\mathbf{=}}\frac{{\mathbf{m}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}{\mathbf{m}}_{\mathbf{n}}{\mathbf{x}}_{\mathbf{n}}}{{\mathbf{m}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}{\mathbf{m}}_{\mathbf{n}}}}$

Y-coordinate of the center of mass:

$\overline{){{\mathbf{Y}}}_{{\mathbf{cm}}}{\mathbf{=}}\frac{{\mathbf{m}}_{\mathbf{1}}{\mathbf{y}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}{\mathbf{y}}_{\mathbf{2}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}{\mathbf{m}}_{\mathbf{n}}{\mathbf{y}}_{\mathbf{n}}}{{\mathbf{m}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}{\mathbf{m}}_{\mathbf{n}}}}$

Moment of inertia:

$\overline{){\mathbf{I}}{\mathbf{=}}{\mathbf{\Sigma }}{\mathbf{m}}{{\mathbf{r}}}^{{\mathbf{2}}}}$

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###### Problem Details

A. Find the coordinates of the center of mass. Find the x-coordinate. Find the y-coordinate.

B. Find the moment of inertia about a diagonal axis that passes through masses B and D.