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Rigid Body Statics

Fundamentals: Are you ready to explore the world of rigid bodies?

In this chapter, we will dive into the fascinating world of rigid body mechanics and explore:

  • The invisible forces that act on objects and set them in motion or slow them down.
  • The secret of cutting free, which allows us to isolate the most important forces acting on an object.
  • The magical free body diagrams, which show us how forces and moments act on an object.
  • The rigid body and its six degrees of freedom, which give it its mobility.
  • The 6 axioms of rigid body statics, which are the foundation for everything we know about objects at rest.

Are you ready to uncover these secrets?

Then buckle up and let's go on an exciting journey into the world of rigid body mechanics!

It's going to be exciting!

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4.6 The Law of Inertia for Rigid Body Statics

The Foundation for the Equilibrium of Rigid Bodies

The law of inertia for rigid body statics is an important principle in rigid body statics. It is Newton's first law, which states that an object will either remain at rest or continue to move at a constant velocity in a straight line unless acted upon by an external force. This means that a rigid object will either stay at rest (\(v=0\)) or move with a constant speed in a straight line (\(v = const\)) as long as no external forces are acting on it. In other words, an object will continue its state of motion unless an external force changes it.

Examples:
  • A resting billiard ball: It just sits there until you hit it.
  • A parked car: It also stays where it is until you start the engine or someone hits it. Unless it's parked on a hill, then it might roll down. But there's an explanation for that too (the force of gravity changes its state of motion), so it's all good.
  • A car driving at a constant speed: As soon as you brake, it slows down. The braking force is the spoiler here, changing its state of motion.
Okay, but why doesn't my bike keep rolling forever when I stop pedaling?

It's simple: There are nasty, invisible forces at work! Air resistance, friction between the tires and the road, and gravity slow your bike down. Eventually, the force of inertia is simply too weak and your bike comes to a stop.

And what about in space?

There is very little friction and gravity there. So an object that was once set in motion would continue to fly forever until it hit another object. How cool is that!

It's that simple! The law of inertia for rigid body statics may be a bit dry, but it explains why the world around us doesn't suddenly descend into chaos. The main thing is, no external force, and everything stays the way it is.

So, enough physics for today.

Now off to the couch and chill - in the spirit of the law of inertia.