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Centre of mass
Intermediate
Mean position weighted by mass.
r_cm = Σm r/MThe centre of mass is the average position weighted by mass; for continuous bodies integrate. It moves as if all external forces act on it.
Rod with masses 2 kg at 0 and 1 kg at 3 m: x_cm = 1 m.
It need not lie within the object.
In more detail
The centre of mass of a system is the mass-weighted average position of its parts. It moves as if all external forces acted on it, which simplifies analysis of complex systems.
Real-world uses
- Designers position the centre of mass of cars and aircraft for stability.
- Athletes manage their centre of mass to balance during jumps.
- Engineers locate the centre of mass of a car to predict how it will handle on a bend and whether it will tip over.
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Frequently asked questions
Can the centre of mass be outside the object?
Yes, for hollow or irregular shapes such as a ring.
Does an internal force move the centre of mass?
No. Only external forces change its motion.
Is the centre of mass always inside an object?
No. A hollow or curved object can have its centre of mass outside its material.
Related topics in Momentum & Collisions
Billiard ball collisions · Ballistic pendulum · Bouncing ball · Velocity of centre of mass · Centre-of-mass frame · Explosions and fragmentation