Caption: Center of mass calculated for objects along a line.
Features:
- The diagram gives an example of
this kind of center-of-mass
calculation.
- The formula
formula for the center of mass of
objects along a line is
x_cm = ∑_i (m_i*x_i) / ∑_i m_i
= ∑_i (m_i*x_i) / m ,
where m_i are the masses of the objects, x_i are centers of mass of the objects, and where m = (∑_i m_i) is the total mass of the system.
- For general 3-dimensional cases, the formula generalizes to
vec_r_cm = ∑_i (m_i*vec_r_i) / ∑_i m_i
= ∑_i (m_i*vec_r_i) / m ,
vec_r stands for position vector in a klutzy html notation.
Image link: Itself.
Local file: local link: center_of_mass_1d.html.
File: Mechanics file: center_of_mass_1d.html.