The center of mass is the spot where an object’s weight is evenly spread out. This spot is super important when things are balanced.

Key Points:

• Static Equilibrium: An object is in static equilibrium when:

  1. The total force going up is equal to the total force going down: $F_{up} = F_{down}$
  2. The total moments (or twists) around any point are equal to zero: $\sum \text{Moments} = 0$

• Example: Think about a seesaw. To keep it balanced, the center of mass needs to be right above the pivot point.

Illustration:

1. If you put a heavy child on one end of the seesaw,
2. You can balance it by moving the lighter child closer to the pivot.

Making sure that forces and moments are balanced helps keep everything stable. This shows just how important the center of mass is for balance and equilibrium.