The three masses shown in the figure(Figure 1) are connected by massless, rigid

Question

The three masses shown in the figure(Figure 1) are connected by massless, rigid rods.

Part A -

Find the coordinates of the center of mass. Find both the x-coordinate and the y-coordinate.

The coordinates should be separated by a comma (i.e. "x,y" ).

Express your answers to two significant figures and include the appropriate units.

Part B -

Calculate the moment of intertia about an axis that passes through the center of mass and is perpendicular to the page.

Express your answer to three significant figures and include the appropriate units.

Part C -

Find the moment of inertia about a horizontal axis that passes through the center of mass.

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

A)
Xcm = (100 x 0 + 200 x 6 + 100 x 12) / (100 + 200 + 100)
= 6 cm

For 200 g, y = SQRT[100 - 36] = 8 cm
Ycm = (100 x 0 + 200 x 8 + 100 x 0) / (400)
= 4 cm

rCM = (6, 4) cm

B)
Distance from r to 200 g = 4 cm
Distance from r to 100 g = SQRT[42 + 62] = 7.2 cm
Moment of inertia about cm = (0.2 x 0.042) + 2 x (0.1 x 0.0722)
= 1.36 x 10-3 kg m2.

C)
Distance from r to each mass = 4 cm
Moment of inertia = (0.2 x 0.042) + (0.1 x 0.042) + (0.1 x 0.042)
= 6.40 x 10-4 kg m2.

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