Science Common Sense

1666 - What is the relationship between the center of mass velocity, the center of mass acceleration, the total momentum of the system, and the external force acting on it?

Imagine you're playing tug-of-war with friends. You all are holding the rope together (like a system). The center of mass is the middle point of all of you.

Here's how the things you asked about are related:

• The center of mass velocity is how fast that middle point is moving.
• The center of mass acceleration is how fast the middle point is speeding up or slowing down.
• The total momentum of the system is how 'hard' the whole team (system) is moving - it's the combination of how fast and heavy you all are.
• The external force is the force another team is pulling on the rope (like the force of the ground, air, or another team).

So here's the big relationship:

The center of mass acceleration is caused by the external force (like the other team pulling). And the change in total momentum of the whole team is equal to the external force times how long the force is applied.

In short, the external force affects the total momentum, which affects how fast the middle point (center of mass) accelerates.