What is the formula for the first moment?

In summary, the first moment divided by the total mass is the center of mass. The first moment is a combination of mass and distance, and the first moment of mass is just mass times distance. The second moment of mass, also known as moment of inertia, is also made up of mass times distance squared. However, the center of mass is not the same as distance, as it is the average position of all the first moment elements divided by the total mass. The position vector of the center of mass can be obtained by adding up all the first moment elements and dividing by the total mass.
  • #1
avito009
184
4
The first moment divided by the total mass is the center of mass. Now I know that a moment is a combination of a physical quantity and distance. So what is the First moment made up of? I know that moment of inertia is made up of mass times the radius (distance) squared.
 
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  • #2
The first moment of mass is just mass times distance.
 
  • #3
So is the second moment of mass "Moment of Inertia"?
 
  • #4
avito009 said:
So is the second moment of mass "Moment of Inertia"?
Indeed it is.
 
  • #5
According to Wikipedia, the first moment divided by the total mass is the center of mass. But as per what you say the first moment is mass times distance so if we divide that by the total mass we get the answer as distance. m*r/m=r. But distance is not the same as centre of mass. How?
 
  • #6
avito009 said:
According to Wikipedia, the first moment divided by the total mass is the center of mass. But as per what you say the first moment is mass times distance so if we divide that by the total mass we get the answer as distance. m*r/m=r. But distance is not the same as centre of mass. How?
That will give you the distance of the center of mass from some reference point (where the distances were measured from).

More precisely, those distances really should be position vectors. To get the position vector of the center of mass, you would add up all the first moment elements (##\Sigma m_i \vec{r}_i##) and then divide by the total mass.
 

1. What is the first moment formula?

The first moment formula, also known as the mean or average, calculates the center point of a set of data by adding all the values and dividing by the total number of values.

2. How do you calculate the first moment?

To calculate the first moment, you must add all the values in the data set and then divide by the total number of values. This can be represented by the equation: sum of all values / number of values = first moment.

3. What is the importance of the first moment?

The first moment is important because it provides a measure of the central tendency of a data set. It can give an idea of the typical value or average value of the data.

4. Is the first moment the same as the median?

No, the first moment and median are not the same. The first moment is the average value of the data set, while the median is the middle value when the data is arranged in ascending or descending order.

5. Can the first moment be negative?

Yes, the first moment can be negative if the data set contains negative values. The first moment is simply a measure of the central tendency and is not limited to positive values.

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