General question about the definition of moment of force (Torque)

[S_Subramaniam]

Homework Statement

My question is related to the understanding of moment of a force.

Relevant Equations

M = F x D

Definition: Moments is a measure of turning effect of a force upon a pivot. My questions: What does it mean if it is a measure of moments? Does it mean the angle of turn? Does it mean the speed of the movement? Does it mean the distance travelled? Let's take a door as an reference.

 

[kuruman]

It is analogous to force. Force is a measure of how easy it is to change the velocity of an object. Moment or torque is a measure of how easy it is to change the angular velocity (relative to a fixed point) of an object. You need both F and D, where D is the shortest distance from the point of application of the force to the pivot point.

For example, to open a door you need to get it to rotate about its hinges. To do that you need a moment M = F × D not just a force F. If D = 0, i.e. you apply the force at the hinges about which you want the door to rotate, the door will not open no matter how large F is.

 

[Orodruin]

Force is a measure of how easy it is to change the velocity of an object. Moment or torque is a measure of how easy it is to change the angular velocity (relative to a fixed point) of an object.

I think this is an unfortunate wording. I would say (inertial) mass is a measure of how hard it is to change the velocity of an object. Likewise, moment of inertia would describe how hard it is to change the angular velocity.

Forces and torques describe how hard the object is being pushed/pulled or twisted.

 

[Lnewqban]

What does it mean if it is a measure of moments? Does it mean the angle of turn? Does it mean the speed of the movement? Does it mean the distance travelled?

Welcome, S_Subramaniam!

You can measure a moment that does not produce any of the above highlighted things.
Just extend one of your arms horizontally in front of you.
The effort that you feel in your shoulder is the moment induced by the weight of your arm acting on a point located about half the length of your arm (and resisted in balance by the muscles and bones of your shoulder.

 

[S_Subramaniam]

So, is moment also a type of force?

 

[kuruman]

So, is moment also a type of force?

No. It has different dimensions from a force.

 

[haruspex]

The effort that you feel in your shoulder is the moment induced by the weight of your arm acting on a point located about half the length of your arm

Not quite. The effort you make is how hard you pull with the muscle in the shoulder; that's a force. That force generates a torque about the shoulder joint to balance the torque the weight of the arm generates about the same joint.

So, is moment also a type of force?

Have you ever used a spanner to undo a tight nut? You can only generate so much force with your muscles, but the longer the spanner shaft the more torque you get from the same force.

 

[jack action]

I think you would like this definition of torque:

Just as the Newtonian definition of force is that which produces or tends to produce motion (along a line), so torque may be defined as that which produces or tends to produce torsion (around an axis). It is better to use a term which treats this action as a single definite entity than to use terms like "couple" and "moment", which suggest more complex ideas. The single notion of a twist applied to turn a shaft is better than the more complex notion of applying a linear force (or a pair of forces) with a certain leverage.

Note that:

In its most basic form, a moment is the product of the distance to a point, raised to a power, and a physical quantity (such as force or electrical charge) at that point

When the distance is raised to the power of one (as with the moment of a force), it usually measures some mean value. (source) For example, the center of mass is the 1st moment of mass normalized by total mass: $\mathbf {R} ={\frac {1}{M}}\sum _{i}\mathbf {r} _{i}m_{i}$ for a collection of point masses. (source)

Similarly, when all forces point in the same direction, you can find the equivalent point of application of the total force: $\mathbf {R} ={\frac {1}{\sum_{i}F_i}}\sum _{i}\mathbf {r} _{i}F_{i}$ for a collection of forces.