What are coordinates of the center of mass for the uniform plate shown in the figure...

Question

Question

10 cm 0 cm 10 cm 10 cm 20 cm 20 cm 10 cm 10 cm What are coordinates of the center of mass for the uniform plate shown in the figure below

Answer 1

Answer #1

Let the plate be divided into left and right portions about the y-axis.

x_cm,left = -5 cm, y_cm,left = 0

x_cm,right = 5 cm, y_cm,right = 0

From symmetry, we can see that the y-coordinate of the center of mass of the whole plate is zero.

A_left = (20 + 20) * 10 = 400 cm²

A_right = (10 + 10) * 10 = 200 cm²

So, x_cm = {[400 * (-5)] + (200 * 5)} / (400 + 200) = -1.67 cm

From symmetry, we can see that the y-coordinate of the center of mass of the whole plate is zero.

Answer 2

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