Center of Mass Calculator

Formula

The formula to calculate the Center of Mass is:

\[ \text{Center of mass} = \frac{m_1x_1 + m_2x_2 + \ldots + m_Nx_N}{m_1 + m_2 + \ldots + m_N}, \frac{m_1y_1 + m_2y_2 + \ldots + m_Ny_N}{m_1 + m_2 + \ldots + m_N} \]

Where:

\( m \) is the mass of each point
\( x \) is the coordinate distance of each point along the x-axis
\( y \) is the coordinate distance of each point along the y-axis

What is Center of Mass?

The center of mass is defined as the point at which if all of the mass of an object was located at that single point, it would behave the same way as the true body of the mass. This concept is essential in understanding the motion of objects and systems in physics.

Example Calculation

Let's assume the following values:

Mass 1 (m1) = 2 kg, x1 = 1 m, y1 = 3 m
Mass 2 (m2) = 3 kg, x2 = 4 m, y2 = 1 m
Mass 3 (m3) = 5 kg, x3 = 2 m, y3 = 2 m

Using the formula to calculate the Center of Mass:

\[ \text{Center of mass (x)} = \frac{2*1 + 3*4 + 5*2}{2 + 3 + 5} = \frac{2 + 12 + 10}{10} = \frac{24}{10} = 2.4 \text{ m} \]

\[ \text{Center of mass (y)} = \frac{2*3 + 3*1 + 5*2}{2 + 3 + 5} = \frac{6 + 3 + 10}{10} = \frac{19}{10} = 1.9 \text{ m} \]

The Center of Mass is (2.4, 1.9) meters.