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Center of mass
Intermediate
The point where the system's mass behaves as concentrated.
x_cm = Σm x/ΣmThe centre of mass is the mass-weighted average position: x_cm = Σm x/Σm. Net external force accelerates it as if all mass were there, no matter how complex the internal motion.
Masses 1 kg at 0 and 3 kg at 4 m: x_cm = 3 m.
It may lie outside the body (a ring).
In more detail
The centre of mass is the average position of a body's mass, and for a uniform body it is at the geometric centre. Forces act on the centre of mass for translational motion.
Real-world uses
- Designers keep the centre of mass low for stable cars and buses.
- Gymnasts control their centre of mass in flips and jumps.
- A baseball bat balances at its centre of mass, which is the point used to describe its overall motion.
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Frequently asked questions
Must the centre of mass be inside the object?
Not always. A ring or boomerang can have its centre of mass outside the material.
Why is the centre of mass useful?
It lets you treat an extended object as a point for translational motion.
Does the centre of mass have to be inside the object?
No. A hollow ring or a boomerang has a centre of mass located in empty space outside the material.
Related topics in Newton's Laws & Forces
Hooke's law limits · Equilibrium of concurrent forces · Torque and equilibrium · Motion of center of mass · Normal force on curves · Constraint forces