# What is Torque and what is correct formula?

• urbano
It's not entirely clear what the issue is. As such, I think it would be best if the original poster were to ask some specific question. Otherwise we'll just keep posting on the subject of torque.

#### urbano

I'm struggling with the concept of torque as I read more I get further confused.

I read some sources and they say torque and moments are interchangeable, yet other sources make a specific effort to keep the two separate. So question one is , what is the difference between torque and a moment ?

The formula for torque...so far I have come across τ= r ×F, but also τ = I ×angular acceleration. I'm unsure which I should be using, and if both, which circumstances determine you to use which.

My overall confusion though is what is torque?

So moment of inertia is the resistance to the force being applied. So is torque the amount of force I need to apply to rotate an object ? or is it the amount of rotational force a force can put on a body ? what is a Nm (Newton meter) how would one see a Newton meter, I presume its not a rate or ratio.

thanks for any help.

"τ= r ×F"
This is, correctly applied, the DEFINITION of torque.
By correctly applying the definition of torque on Newton's second law of motion, F=ma, we gain the RESULT
"τ=I ×angular acceleration" for the rigid body.

"ma" in F=ma is often called "the rate of change of (linear) momentum", whereas "I ×angular acceleration" is often called "the rate of change of angular momentum".

urbano said:
I read some sources and they say torque and moments are interchangeable, yet other sources make a specific effort to keep the two separate. So question one is , what is the difference between torque and a moment ?
To some, torque and moment (of force) are synonyms. To some engineers, they're not. They distinguish between moment of force and torque. So, yes, there is a potential for confusion. This is physicsforums.com, not engineeringforums.com, so at this site it's best to stick with the nomenclature used in physics.

The formula for torque...so far I have come across τ= r ×F, but also τ = I ×angular acceleration. I'm unsure which I should be using, and if both, which circumstances determine you to use which.
By way of analogy, consider a mass attached to a spring. On one hand, Hooke's law describes the force exerted by the spring on the mass is F=-kx, where x is the displacement from the spring's relaxed position. On the other hand, we have F=ma from Newton's laws of motion. Presumably you aren't confused by F=-kx versus F=ma, so why should you be confused by τ=r×F versus τ=Iα?

In the spring mass system, F=ma is a kinematic description of what transpires. F=-kx is a dynamic description of what's happening. Put the two together and you get a second order differential equation, ##m\frac{d^2x(t)}{dt^2} = -k x(t)##. The same happens with rotational motion. τ=r×F is a dynamic description of torque. τ=Iα is a kinematic description. Put the two together and you get a second order differential equation that describes what's happening rotationally.

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urbano said:
I'm struggling with the concept of torque as I read more I get further confused.

I read some sources and they say torque and moments are interchangeable, yet other sources make a specific effort to keep the two separate. So question one is , what is the difference between torque and a moment ?

The formula for torque...so far I have come across τ= r ×F, but also τ = I ×angular acceleration. I'm unsure which I should be using, and if both, which circumstances determine you to use which.

My overall confusion though is what is torque?

I view the two formulas as cause and effect: If you apply a force $\vec{F}$ at position $\vec{r}$ on a rigid object, it will cause the object to increase its rate of angular velocity $\omega$ according to the formula:

$\vec{r} \times \vec{F} = I \cdot \dot{\vec{\omega}}$

(In general, $I$ is a tensor, so the operator $\cdot$ is a tensor operation.)

The first two posts are excellent but may be a bit advanced if your are just starting this
subject. So study them carefully.

[Third post made while I was typing this...]

Some reasonable explanation and details are here:

http://en.wikipedia.org/wiki/Torque

By definition, torque τ = r × F. Therefore torque on a particle is equal to the first derivative of its angular momentum with respect to time.

You can also check any good introductory physics textbook like Halliday and Resnick.

So moment of inertia is the resistance to the force being applied.

that's the idea, but I'd say ...is the ROTATIONAL resistance to the force...Trying to rotate a body usually takes a different force than trying to move the body linearly.
The resistance to a linear force is referred to as 'inertia'.

So is torque the amount of force I need to apply to rotate an object ?

yes, but at some specified distance 'r' as described in the Wikipedia link...
Via Tau [torque] = r x F torque varies both from the force F and the distance of the applied force from the point/axis of rotation.

what is a Nm (Newton meter) how would one see a Newton meter, I presume its not a rate or ratio.

refer to the prior equation.
I assume you know a 'Newton' is a unit of force in the MKS system. A Newton meter is such a force applied at a specified distance from the axis of rotation. You can't 'see' such but you may be able to observe the result...rotational motion. Analogously, a Newton [meaning applied linearly] might move an object, say against friction or gravity.

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stevendaryl said:
$\vec{r} \times \vec{F} = I \cdot \dot{\vec{\omega}}$
Even more generally, the left hand side should be a sum over all external forces, and the right hand side should be the derivative of angular momentum:
$$\sum \vec r \times \vec F = \frac d{dt} (I\cdot \vec \omega)$$
In the special case that the moment of inertia can be treated as a constant scalar, this becomes
$$\sum \vec r \times \vec F = I\dot{\vec{\omega}}$$
This is the appropriate equation for introductory level physics.

(In general, $I$ is a tensor, so the operator $\cdot$ is a tensor operation.)
The original poster is asking some very introductory level questions, so it's best to ignore the tensorial nature of the moment of inertia. Besides, your equation is not correct if you do look at moment of inertia as a tensor.

Posts which are a bit above the level of a high school / freshman level understanding have been split to a different thread, [thread]711348[/thread].

Please keep remaining posts on topic and in line with what a young person taking a first year class in physics would understand.

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## 1. What is torque and why is it important?

Torque is a measure of the twisting force that causes an object to rotate. It is important because it helps us understand the rotational motion of objects and is essential in many scientific and engineering applications.

## 2. What is the correct formula for torque?

The correct formula for torque is τ = r x F, where τ is the torque in Newton-meters (Nm), r is the distance from the axis of rotation to the point where the force is applied, and F is the force in Newtons (N).

## 3. Can you explain the role of lever arm in the formula for torque?

The lever arm, or the distance between the point where the force is applied and the axis of rotation, is a crucial component in the formula for torque. It determines the effectiveness of the force in causing rotational motion.

## 4. How is torque different from force?

Force is a vector quantity that measures the push or pull on an object, while torque is a vector quantity that measures the twisting force on an object that causes it to rotate. They are related, but have different effects on an object's motion.

## 5. Can you provide an example of torque in everyday life?

A common example of torque in everyday life is using a wrench to loosen a bolt. The force applied to the handle of the wrench creates a torque that loosens the bolt, allowing it to rotate. Another example is opening a door by pushing on the handle, which creates a torque that causes the door to rotate on its hinges.
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