# Why is torque perpendicular to the force applied?

• MRzNone
In summary, the direction of torque is perpendicular to the force and crosses the rotational point because this is how torque is defined and it turns out to be a useful definition.
MRzNone
I understand the right hand rule and the equition, but why is the direction of the torque perpendicular to the force on the counter clockwise side of the force and crossing the rotational point?

Because this is how torque is defined and it turns out to be a useful definition. You could just as well have defined it with a minus sign, but this would have had other consequences in other formulas.

But, definitions are derived right? Can you explain me how? They are seemingly irrelevant to me.

MRzNone said:
But, definitions are derived right?
No. Definitions are not derived by construction. If it is possible to derive something, you do not need to define it.

its a convention but i think you can feel that intuitive having thought over this -
look,
if you a screw and over it you have a nut ,tightly fitted ; and you are to undo it, using a spanner !
So, you will be rightly placing the spanner and forcing it to rotate it in counter clockwise sense about the screw
doing that you will be undoing the tightening , making the nut move towards you
so now you can think that your force on the spanner materialized into the outward movement of the nut (the direction of torque) !

How is it now ?!

Shreyas Samudra said:
So, you will be rightly placing the spanner and forcing it to rotate it in counter clockwise sense about the screw
doing that you will be undoing the tightening , making the nut move towards you
so now you can think that your force on the spanner materialized into the outward movement of the nut (the direction of torque) !

Note that this intuition is solely based on the convention of making nuts/screws with a particular handedness.

I second everything that Orodruin said, and I would like to add that the definition ensures that torque is to angular momentum what force is to momentum. What I mean by that is that force is the time derivative of momentum, and torque is the time derivative of angular momentum:
$$\dot{\mathbf L} =\frac{d}{dt}\left(\mathbf r\times(m\dot{\mathbf r})\right) =\mathbf r\times (m\ddot{\mathbf r}) =\mathbf r\times\mathbf F=\mathbf\tau.$$

And just to add to that, the relation would still hold if we defined both torque and angular momentum with a minus sign relative to the usual definition.

Is the question about the fact that the torque is perpendicular to the force or about the "clockwise" part?

have
MRzNone got that

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

Torque is a measure of a force's ability to rotate an object around an axis. It is important because it helps us understand how forces affect the motion and stability of objects.

## 2. How is torque calculated?

Torque is calculated by multiplying the force applied by the distance from the axis of rotation to the point where the force is applied. The unit of torque is Newton-meters (Nm) in the SI system.

## 3. Why is torque perpendicular to the force applied?

Torque is perpendicular to the force applied because it is the product of two vectors: the force vector and the distance vector. The distance vector is always perpendicular to the force vector, resulting in a perpendicular torque vector.

## 4. Can torque ever be parallel to the force applied?

No, torque can never be parallel to the force applied. This is because the distance vector is always perpendicular to the force vector, and torque is the result of multiplying these two vectors together. Therefore, the torque vector will always be perpendicular to the force vector.

## 5. How does torque affect an object's rotation?

Torque is responsible for causing an object to rotate around an axis. The direction of the torque vector determines the direction of the rotation, and the magnitude of the torque determines how fast the object will rotate.

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