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Center of Mass

Consider a system of N particles with masses m₁, m₂, ..., m_i, ..., m_N. Each particle has coordinates (x_i, y_i).

System mass is, and the coordinates of the center of mass, (X_com, Y_com) are

1. Find the center of mass of the system of two objects shown.

2. Find the COM coordinates for a circle of radius R with a circle of radius R/2 removed.

3. Continuous, non-symmetric objects. Formally the definitions become

To evaluate this for x, you must (1) choose a narrow slice of the object a constant distance x. (2) give the location, x, and width dx, (3) express the infinitesimal mass of the slice in terms of x, dx, and other constants. (4) choose the limits of the integral, and (5) evaluate.

Find the COM coordinates for a uniform isosceles triangle of base H and length L.