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Motion of center of mass
Intermediate
The centre of mass moves as if all external forces act on it.
The centre of mass of a system moves as a point of mass M under the total external force: F_ext = M a_cm. Internal forces such as explosions don't change it.
A thrown wrench spins complexly but its centre of mass follows a parabola.
An exploding firework's centre of mass keeps its projectile path until things hit the ground.
In more detail
The centre of mass moves as if all the mass were concentrated there and all external forces acted on it. Internal forces do not change its motion.
Real-world uses
- A fireworks shell's centre of mass follows a parabolic path even as fragments scatter.
- Analysing exploding objects or collisions uses centre-of-mass motion.
- A thrown spanner tumbles in the air, but its centre of mass follows a simple parabola as if all the mass were there.
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Frequently asked questions
Does an exploding object's centre of mass still follow a parabola?
Yes, if no external forces act besides gravity.
What forces change the centre-of-mass motion?
Only external forces, not forces between parts of the system.
Why does the centre of mass follow a parabola?
Only external forces change the motion of the centre of mass, and gravity acts as a single force on the whole body.
Related topics in Newton's Laws & Forces
Equilibrium of concurrent forces · Torque and equilibrium · Center of mass · Normal force on curves · Constraint forces · Newton's laws and inertial frames