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Physics

How do you find the center of mass in objects?

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05/03/2008

The center of mass is defined as x_CM = (m_1x_1+m_2x_2+...+m_nx_n)/(m_1+m_2+...+m_n), where the x_i are the (vector) location of the particles and m_i are their masses. If the object is a continuous media (not composed of a countable set of particles), we define x_CM=integral ( rho(x)*x dx) / integral ( rho(x) dx), where rho(x) is the density at point x and the integral is to be preformed over all of space (i.e. wherever rho is positive). If you have an object and want to practically find the center of mass. Attach a wire to some point on it and hang it from that point. Then draw a line straight down from the hanging point and threw the body. Do this a few times with different hanging points. The intersection of the lines is the center of mass.