Static moment VS Moment of inertia - what's the difference?

• Femme_physics
In summary: Could you give an example of when area moment of inertia would be more relevant than mass moment of inertia?A beam with mass M and a length L is subjected to a horizontal force F applied at a distance D from the beam's center of gravity. Find the area moment of inertia of the beam.In this scenario, the area moment of inertia would be more relevant because the force is being applied at a distance from the center of gravity, which would result in a change in the beam's rotational inertia.
Femme_physics
Gold Member
Static moment VS Moment of inertia -- what's the difference?

What's the difference between moment of inertia and static moment? How does it differ in calculations?

I think we could say that a static moment has nothing to do with motion...it is simply the result of a force being applied at a pivot via a lever...so force times distance is the moment.

Moment of inertia is a property of the body.

Moment of inertia is to rotation what mass is to linear translation.

If you want to push something a distance, it will take you a while to getting moving because you have to overcome the inertia of the resting mass...

If you want to rotate something for an angle, you will need to overcome the body's "angular" mass...this is the moment of inertia, that you are having to overcome and it is not just the mass.

I think we could say that a static moment has nothing to do with motion...it is simply the result of a force being applied at a pivot via a lever...so force times distance is the moment.
You mean that a static moment is just a moment that doesn't cause motion?

Well, yes and no, all I am saying is that the CONCEPT of moment does not have anything to do with motion...it could cause motion or could not...but that has nothing to do with the DEFINITION of moment...

the thing is that when a moment causes motion, they start calling it torque, even though is basically the same concept...force times distance.

So, to be in agreement with their definitions...in a static system, the moment is just there and nobody is rotating

When there is rotation and the force is applied continuously and hence it needs to also rotate so that it can continue to be applied in the same spot...then, the force needs to also rotate ...in this case, this "moment" is called torque.

They are not the same concept at all.

A moment (or a torque) has units of force*distance (N*m, J, ft-lb, etc.) is exactly that. It's an force applied at a point a certain distance away from another point that causes a rotation. A static moment is a moment caused in a static system. An example would be a force applied at the end of a cantilever beam. It induces a static moment about the fixed end of the beam. There is no motion in the system, but there is a moment applied.

The moment of inertia is a property of the beam. It has units of distance^4 and it can be thought of as a measure of the resistance to rotation about a certain axis. For example, it's much easier to rotate a pencil about its centroid, but harder to rotate about either end. The moment of inertia is different for each of those cases, so you could say it's a measure of rotational resistance.

Oh, I see...I think we now need to differentiate the two moments of inertia...yes, there are two: area moment of inertia and mass moment of inertia.

In my initial reply, I made comments regarding the concept of mass moment of inertia, which, by the way, it has units of mass x (distance^2).

tim, on the other hand, is talking about the area moment of inertia (units of distance^4)...

...Probably Tim's answer is more along what the OP was looking for talking about static moment in the first place and possibly having to apply this to textbook exercises with beams, etc...in those cases, you are concern with area moments of inertia...

sorry about the tangent...it does not hurt, though.

gsal, I totally forgot to mention in my post about the two kinds of moment of inertia. Good catch there. I just assumed the OP was talking about statics and usually you don't deal mass moment of inertia as much as the area moment of inertia in statics.

Just wanted to interject that all my engineering professors hated the term "area moment of inertia" because it has little, if anything, to do with the concept of inertial mass. They preferred the term "second moment of area". I guess I learned it first as "area moment of inertia", so I use that.

Your words are slightly ambiguous.

I expect the word "moment" without "inertia" behind it, to be a moment of force times distance.

I expect the word "moment" with "inertia" behind it, in your case, to be the area moment of inertia.

Do you have examples of where they are used?
Because we will be able to deduce from the context what is intended.

1. What is the difference between static moment and moment of inertia?

Static moment and moment of inertia are two different concepts that are often confused with each other in physics. While they both involve the concept of force and motion, they refer to different properties of an object.

2. How is static moment defined?

Static moment is defined as the product of a force and its distance from a fixed point. It is a measure of the turning effect or torque of a force on an object.

3. What is the formula for calculating static moment?

The formula for calculating static moment is M = F x d, where M is the static moment, F is the force applied, and d is the distance from the fixed point.

4. How is moment of inertia defined?

Moment of inertia is defined as the measure of an object's resistance to changes in its rotational motion. It is affected by both the mass and the distribution of mass in an object.

5. What is the equation for calculating moment of inertia?

The equation for calculating moment of inertia varies depending on the shape and distribution of mass of the object. Some common equations include I = mr^2 for a point mass rotating around an axis, and I = 1/12ml^2 for a thin rod rotating around its center of mass.

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