What is torque exactly?

[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?

 

[Lnewqban]

It is a concept.

Please, see:
http://hyperphysics.phy-astr.gsu.edu/hbase/rotv.html#rvec1

 

[as2528]

It is a concept.

Please, see:
http://hyperphysics.phy-astr.gsu.edu/hbase/rotv.html#rvec1

Thank you! I think I understand it better now.

 

[A.T.]

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.

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.

 

[malawi_glenn]

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? :)

 

[A.T.]

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 is asking why torque is perpendicular to the force, not why you need a force component perpendicular to radius in order to produce torque.