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Centre-of-mass frame
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Frame where total momentum is zero, simplifying collisions.
In this frame total momentum is zero, so collisions look symmetrical: particles approach with equal and opposite momenta. Switching to this frame simplifies analysis and particle-physics calculations.
A fixed-target collision is equivalent to a head-on collision in the CM frame.
The CM frame is inertial only if there is no net external force.
In more detail
The centre-of-mass frame moves with the centre of mass of a system. In this frame the total momentum is zero, which often makes collision problems much simpler.
Real-world uses
- Particle physicists analyse collisions in the centre-of-mass frame.
- Engineers simplify two-body collision problems by choosing this frame.
- Particle physicists analyse collisions in the centre-of-mass frame, where the total momentum is zero and the calculation is simpler.
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Frequently asked questions
Why is momentum zero in this frame?
Because the frame moves with the centre of mass, so the total momentum relative to it is zero.
Do collisions look different in this frame?
The motion looks simpler, but the physics does not change between frames.
Is the centre-of-mass frame always the best?
It is very useful for collisions, but for a single body moving freely the laboratory frame is often simpler.
Related topics in Momentum & Collisions
Bouncing ball · Centre of mass · Velocity of centre of mass · Explosions and fragmentation · Variable mass: rocket equation · Thrust