The centre of mass is an imaginary point in an object where its entire mass is assumed to be concentrated. When an object moves, this point follows the laws of motion just like a single particle.

The Concept of Motion

Imagine throwing a spinning hammer in the air. The hammer rotates wildly, but its centre of mass follows a smooth, curved path called a parabola. Even if the object is complex, the centre of mass behaves as if a single force were pushing a single dot. This simplifies complex physics problems by ignoring the rotation of individual parts and focusing on the overall displacement.

Newton’s Law for Centre of Mass

The motion of the centre of mass is governed by the total external force applied to the system. The mathematical formula is: F_ext = M * A_cm. Here, 'F_ext' is the sum of all outside forces, 'M' is the total mass of the object, and 'A_cm' is the acceleration of the centre of mass. If no external force acts on the system, the centre of mass will either stay at rest or move in a straight line at a constant speed.

Real-World Examples

• Exploding Firework: When a firework explodes in mid-air, the pieces fly in many directions. However, the centre of mass of all those pieces continues to follow the same arc the firework was on before the blast.
• Diving Athletes: When a diver tucks their body into a ball mid-air, their body rotates fast, but their centre of mass still follows the exact path of a simple projectile.
• Two Skaters: If two ice skaters push off each other, they move in opposite directions, but their shared centre of mass remains unmoved if they started from rest.