Center of Mass
Place masses, find COM trajectory. Builds on Momentum & Impulse.
A firecracker is launched as a projectile, following a perfect parabolic arc. At the top of its arc, it explodes into many pieces.
What path does the center of mass of the pieces follow after the explosion?
The center of mass continues on the SAME parabola! The explosion forces are internal to the system — they redistribute momentum among pieces but don't change the total. Since external force (gravity) is unchanged, the center of mass follows the same trajectory. Individual pieces go everywhere, but their average stays on track.
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Launch a firecracker and watch it explode. The pieces scatter but the center of mass (golden dot) keeps tracing the parabola perfectly.
x_cm = Σmᵢxᵢ / M
A wrench thrown across a room tumbles wildly — but its center of mass traces a perfect parabola. The tumbling is internal; the parabola is external (gravity).
In the Fosbury Flop, a high jumper's body arcs over the bar while their center of mass actually passes UNDER it! The COM can be outside the body.
The Earth and Moon orbit their common center of mass, which is about 4,670 km from Earth's center — still inside Earth, but not at the center.
After a firework shell explodes, the center of mass of all the sparks continues falling parabolically downward — even as the sparks fly in every direction.
“The center of mass is physics' ultimate simplification. No matter how chaotic a system becomes internally, its COM moves with peaceful, predictable simplicity.”
COM Tracker
Place masses on a plane and watch the center of mass update. Then set them in motion and watch COM follow a smooth path even as individual masses move chaotically.
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Place two masses and give them opposite velocities. They fly apart but the center of mass stays perfectly still (or moves uniformly). Now add gravity and watch COM trace a parabola while the masses do their own thing.
The center of mass is a 'ghost point' that obeys Newton's laws perfectly, even when the actual objects are doing wild, chaotic things.