Can a Moment Couple Really Impact an Entire Building Equally?

[Noesis]

I have been learning about moment couples and all of their greatness...but even after seeing and verifying myself the mathematical proof I just can't bring myself to fathom the fact that a moment couple acts as a 'free vector.'

How can every single point on an object feel the same moment at the same time?

You're telling me if I had a massive building let's say...and I decided to exert a little moment couple ALLLL the way on the top floor, on the very edge of the building let's say...that the same moment would be felt all the way at the very bottom?

In fact that every molecule (let's just say the building is a large chunk of rectangular prism stuff and is totally homogeneous) in the building would feel the same moment concurrently?

Might be an extreme example...but the laws of physics should hold true regardless right?

I'm just having trouble conceptualizing this...believing it even. Any words of wisdom would be great.

 

[Valkarie]

The concept of a moment couple acting as a free vector is based on the idea that moments are vectors, meaning they have magnitude and direction but no specific point of application. This means that the moment caused by a moment couple is uniform throughout the entire object, no matter where it was applied. So, if you were to apply a moment couple at the top of a building, the same moment would be felt all the way at the bottom. This is because the moment couple produces a force that acts in a uniform manner all around the object, regardless of the point of application.

 

[piercas]

I understand your struggle to conceptualize the idea of a moment couple acting as a free vector. It can be a difficult concept to grasp, especially when we are used to thinking in terms of forces acting on specific points on an object.

First, it's important to remember that a moment couple is not a force, but rather a torque. It is a rotational force that is applied to an object. And unlike a single force, which has a specific point of application, a moment couple acts on an entire object.

Think of it this way: when a moment couple is applied to an object, it creates a rotational force that is distributed throughout the object. This force is not focused on one specific point, but rather acts on every point in the object. This is why every molecule in the building in your example would feel the same moment concurrently.

Additionally, it's important to consider the concept of equilibrium. When a moment couple is applied to an object, it creates a torque that is equal in magnitude but opposite in direction to any other torques acting on the object. This is what allows the object to remain in equilibrium and not rotate.

So, while it may be difficult to imagine, the laws of physics do hold true for moment couples. They are a fundamental concept in mechanics and have been proven through mathematical analysis and experimental observations. Keep exploring and studying the concept, and I'm sure you will eventually come to fully understand and believe in the power of moment couples.