What is the direction of torque when n is not perpendicular to r?

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SUMMARY

The discussion clarifies the direction of torque when the unit vector n is not perpendicular to the position vector r. The general formula for torque is defined as n.(r×F), where n is a unit vector, r is the position vector, and F is the applied force. When n is not perpendicular to r, the torque's direction is still determined by the vector cross product r×F, which remains perpendicular to both r and F. The component of torque along the axis defined by n represents the effective torque about that axis.

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Aziza
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My book defines the general formula for torque as:

n.(r×F), where . means dot product, n is a unit vector along the line about which you are taking the torque, F is the force acting at some point, and r is the vector from the line to the point at which the force acts. So I know that when the line about which you are taking the torque is perpendicular to r, then the torque is defined as r×F, so it has a direction perpendicular to r and F.

However, what would be the direction of the torque if n is not perpendicular to r? n.(r×F) does not reveal the direction since it is just a scalar. Would the direction still be just r×F in this general case?
 
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nvm i think i just answered my question...if you just consider the torque about each axis then its obvious that the direction of the torque is just the direction of r×F
 
Hi Aziza! :smile:

Yes, what your book defines as the torque about an axis is really the component of the torque along that axis. :wink:
 

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