Intuition behind centre of mass equation for a rigid body

In summary, an integral is a mathematical concept that represents the area under a graph. It is calculated by summing f(x) * delta x, with delta x approaching zero. It is not specifically related to change in mass and displacement, but rather a more general concept.
  • #1
Pochen Liu
52
2
Homework Statement
I don't understand how we move from the discrete equation to the continuous one
Relevant Equations
I don't know how to type this in
So my basic understanding of an integral is that it finds the area underneath a graph.

I understand the idea behind an integral being the summation of f(x) * delta x, where delta x approaches zero.

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If I look at the integral it's telling me that there's a change in mass that is being multiplied by its displacement?
Supposedly it's meant to represent a uniform distribution but I can't see it. If someone could clear up my intuition behind this that would be great :)
 
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  • #2
Pochen Liu said:
change in mass that is being multiplied by its displacement?
No, it is an element of mass multiplied by its displacement from the origin.

Pochen Liu said:
it's meant to represent a uniform distribution
No, it is quite general.
 

What is the definition of centre of mass?

The centre of mass of a rigid body is the point where the entire mass of the body can be considered to be concentrated. It is the average position of all the mass in the object.

How is the centre of mass calculated for a rigid body?

The centre of mass is calculated by taking the weighted average of the positions of all the particles in the body. This means that the position of each particle is multiplied by its mass and then divided by the total mass of the body.

Why is the centre of mass important in physics?

The centre of mass is important because it helps us understand the overall motion of a rigid body. It is also used in calculations of rotational motion and stability of objects.

What factors affect the centre of mass of a rigid body?

The centre of mass of a rigid body is affected by the distribution of mass within the body. If the mass is evenly distributed, the centre of mass will be at the geometrical centre of the body. However, if the mass is unevenly distributed, the centre of mass will be closer to the denser regions of the body.

Can the centre of mass be located outside of the body?

Yes, the centre of mass can be located outside of the body if the mass distribution is not symmetrical. This can occur in objects with irregular shapes or in cases where the density of the object is not uniform.

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