Center of Mass Calculator
The center of mass is the weighted average position of all the mass in a system. For two objects, a 5 kg mass at x=0 and a 3 kg mass at x=4 m have their center of mass at x = (5*0 + 3*4)/(5+3) = 1.5 m, closer to the heavier object. This calculator handles up to 5 point masses in two dimensions.
The center of mass formulas for a system of point masses are:
Xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn)
Ycm = (m1y1 + m2y2 + ... + mnyn) / (m1 + m2 + ... + mn)
Or more compactly: Rcm = Sum(mi * ri) / Sum(mi)
**Why Center of Mass Matters:** - **Stability:** An object tips over when its center of mass is no longer above the base of support (this is why loaded trucks and SUVs are more prone to rollover) - **Orbital mechanics:** Two orbiting bodies rotate around their common center of mass (the barycenter). The Earth-Moon barycenter is about 4,670 km from Earth's center - **Sports:** A high jumper arches their back so their center of mass passes under the bar while their body clears it (the Fosbury Flop technique) - **Engineering:** Crane load calculations, vehicle weight distribution, and satellite balancing all rely on center of massTo find the center of mass of an irregular object experimentally, hang it from two different points and draw plumb lines. The center of mass is where the lines intersect.