\[x_{cm}=\frac{m_1x_1+m_2x_2}{m_1+m_2}\]
Variables
xcmcenter of mass position (m)
m1mass of segment 1 (kg)
x1position of segment 1 center (m)
m2mass of segment 2 (kg)
x2position of segment 2 center (m)
Description
What is this formula?
This formula calculates the center of mass position for a system composed of two segments or bodies along a single axis. It determines the balance point of the system.
When to use it
Use this formula in biomechanics, kinesiology, robotics, or physics when analyzing body segment positioning and balance.
Example
Two body segments have:
m1=8 kg
x1=0.3 m
m2=12 kg
x2=0.8 m
Formula:
xcm=((m1*x1)+(m2*x2))/(m1+m2)
Substitution:
xcm=((8*0.3)+(12*0.8))/(8+12)
Result:
xcm=0.6 m
The combined center of mass is located at 0.6 m.
Applications
- Human balance analysis
- Biomechanics
- Prosthetic design
- Robotics
- Sports science