# What is the Purpose of Torque?

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• as2528
In summary: It is just a mathematically efficient convention to represent torque and other angular quantities like that.
as2528
TL;DR Summary
Why is torque perpendicular to force and radius?
From what I understand about torque, it is basically the power of the force to cause a change in an object's rotational motion. It is easier to cause this change when the force is applied further from the point of rotation than closer, which is why it is difficult to open a door by pressing a millimeter from the hinges, but much easier by pushing on the door a meter from the hinges.

However, I do not understand why the torque is the cross product of the force and radius. If I use a wrench and push on it, why is torque perpendicular to the force? I thought it would be in the same direction as the force. But it is perpendicular which seems to be counterintutitive as neither the force, the radius, or the change in angular motion is involved in that direction. What is torque meant to calculate then, and how does it make sense?

as2528 said:
From what I understand about torque, it is basically the power of the force to cause a change in an object's rotational motion.
Force is the rate of transfer of linear momentum.
Torque is the rate of transfer of angular momentum.

Note that angular momentum doesn't imply that something is rotating.

as2528 said:
However, I do not understand why the torque is the cross product of the force and radius.
It's just a mathematically efficient convention to represent torque and other angular quantities like that.

mathguy_1995, cancerman1, davyzhu and 3 others
as2528 said:
why is torque perpendicular to the force?

Have you tried to make a wrench and bolt rotate by pushing the wrench towards the pivot point of the bolt? :)

as2528 and topsquark
as2528 said:
why is torque perpendicular to the force?
malawi_glenn said:
Have you tried to make a wrench and bolt rotate by pushing the wrench towards the pivot point of the bolt? :)
@as2528 is asking why torque is perpendicular to the force, not why you need a force component perpendicular to radius in order to produce torque.

as2528 and topsquark
Think of a torsion spring....like a spring of a mousetrap. the trap is set by bending the ends of the springs in opposite directions and perpendicular to the axis of the spring. Then along the axis of the spring potential energy is stored in the form of the spring twisted...or torsion.

Last edited:
as2528 said:
TL;DR Summary: Why is torque perpendicular to force and radius?

But it is perpendicular which seems to be counterintutitive as neither the force, the radius, or the change in angular motion is involved in that direction. What is torque meant to calculate then, and how does it make sense?
The vector representing torque c is parallel to the rotation axis (if the force b was free to move).

Furthermore, its direction indicates in what direction it would rotate (if the force b was free to move).

Finally, its length - as always - represents its magnitude.

https://en.wikipedia.org/wiki/Cross_product#Definition said:
The cross product a × b is defined as a vector c that is perpendicular (orthogonal) to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span.

This way, you can add (vectorially) the different torques in a model and get the resultant torque which will be parallel to the resultant rotation axis, indicating its magnitude and rotation direction. Multiple combinations of different force and position vectors could represent that resultant torque.

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