Torque, point or axis of rotation

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Torque is calculated with respect to a point in 2D and an axis in 3D, leading to confusion when relating torque and angular momentum, which may reference different axes. The formula T = r × F indicates that the torque direction is determined by the axis of rotation, which is perpendicular to both the position vector r and the force vector F. In 3D, the challenge arises from the infinite axes of rotation possible through a point, but the torque vector aligns with the specific axis of rotation. The discussion also touches on the concept of pseudovectors, which are relevant in understanding torque and angular momentum. Overall, clarity on the relationship between torque, angular momentum, and their respective axes is essential for proper application in physics.
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Hi,

1) Do we calculate torque with respect to a point or with respect to an axis?

I have read them both in different resources, and so I am confused!

2) If we calculate torque with respect to an axis, many introductory textbooks discuss the motion of the gyroscope by considering how the torque affects the angular momentum, but there is a problem that the angular momentum is specified with respect to a different axis of rotation than that of the torque (The angular momentum is about the axis of the wheel, while the torque is about the axis passing through the pivot and perpendicular to the first one); how can we resolve this?

Thanks to any helps.
 
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In 2D, a torque is about a point.
In 3D it is about an axis.

Just the same way that a rotation is about a point in 2D and an axis in 3D.
But note: angular momentum and torque are not like regular vectors.
per your example, the same texts should show you the math of how the torque affects the angular momentum.
 
Simon Bridge said:
In 2D, a torque is about a point.
In 3D it is about an axis.

Thanks to your reply.

My problem is that when applying the formula T = r × F in 3D, r is determined with respect to a point where there are infinite axis of rotations passing through this point, so T is determined with respect to which axis?
 
My problem is that when applying the formula T = r × F in 3D, r is determined with respect to a point where there are infinite axis of rotations passing through this point, so T is determined with respect to which axis?
... the axis of rotation of course... which is a vector perpendicular to both r and F... points in the same direction as the pseudovector T. That is what the direction part of the cross product is for.
 
Simon Bridge said:
... the axis of rotation of course... which is a vector perpendicular to both r and F... points in the same direction as the pseudovector T. That is what the direction part of the cross product is for.

What is meant by pseudovector?
 
Thank you very much.
 

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