# Definition of moment

1. Mar 1, 2017

### hndalama

1. The problem statement, all variables and given/known data
The book I am reading says that given a point mass(m) at the point x, the quantity mx is the "moment about the origin)"
It then defines the moment of a collection of points as M = m(1)x(1) + m(2)x(2) + .... m(n)x(n)
where m(1) = mass of first point and x(1)=distance of first point from origin

It then defines that the center of gravity (X) of the point masses is the moment (M) divided by the total mass(m). X=M/m
This is all in one dimension,i.e. like the point masses are on a seesaw(x axis)
2. Relevant equations

3. The attempt at a solution
Previously I learnt that moment = torque. In one dimension, torque is defined as the force times the distance from the pivot point. hence torque of a point mass from the origin is Fx.
if moment= Fx then how can the "moment about the origin" be mx? mass is not a force.

2. Mar 1, 2017

### haruspex

The term "moment" is used in more than one way. The book you are reading is describing moment of mass. Torque is the moment of a force. Moment of inertia is also called the second moment of mass.

3. Mar 1, 2017

### hndalama

Okay, but when we say "moment" of mass, "moment" of force or "moment" of inertia, what does the word moment mean in these phrases?

4. Mar 1, 2017

### haruspex

They all come from the common English usage of 'moment' to mean importance, significance. Similarly momentum.
The extension to different orders of moment is common to mechanics and statistics. Given any quantity f(x) which might vary according to a parameter x, we may speak of the zeroth moment, ∫f(x).dx, the first moment, ∫f(x)x.dx, the second moment ∫f(x).x2.dx, etc. E.g. "second moment of area".

5. Mar 2, 2017

### hndalama

Thank you, I understand that. I have one more question if you don't mind. When the book talks about the moment of mass in two dimensions, it defines M(x) as the moment of mass about the "x axis" and M(y) about the "y axis." so by my understanding, on cartesian coordinates, two points of equal mass located at the points (3,3) and (3,6). will have the same moment of mass about the y axis despite having different distances from points on the y axis.

This is different to moment of force and moment of inertia which are defined with distances from a point. so my question is why is moment of mass defined with distances from an axis instead of a point?

6. Mar 2, 2017

### haruspex

Is that what you meant? (3,3) and (3,6) are the same distance from the y axis.
No, moment of inertia is also defined in relation to an axis, namely, an actual or potential axis of rotation.
Moment of force is often about a specified axis, but can be about a point. The other difference is that it is a vector, whereas the other two are scalars. This is related to the parity of the exponent on the displacement vector: mr0 and mr2 are necessarily scalar, whereas mr1 is naturally a vector.

7. Mar 2, 2017

### David Lewis

Moments are always taken with respect to a line. With polar moments (as opposed to rectangular moments) the moment arm can be measured from the point where the reference axis intersects the plane of rotation.
You could have the moment of the mass about some point. In elementary situations x can be the magnitude of a displacement vector running from the reference axis to the mass.

8. Mar 2, 2017

### haruspex

Only for scalar moments. As I wrote in post #6, vector moments, such as torque, are about a point. Similarly, the first moment of mass about a point gives the mass times the displacement vector from the point to the mass centre.
In many situations, though, we are only interested in the component of the vector parallel to a given axis.

9. Mar 4, 2017