Torque, point or axis of rotation

In summary, 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?
  • #1
bgq
162
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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?
 
  • #7
Thank you very much.
 

What is torque?

Torque is a measure of the amount of force applied to an object that causes it to rotate around an axis or pivot point. It is usually measured in units of newton-meters (N·m) in the metric system and foot-pounds (ft·lb) in the imperial system.

What is the point or axis of rotation?

The point or axis of rotation is the fixed point around which an object rotates. It can be a physical point, such as the center of a wheel, or an imaginary point, such as the center of mass of an object.

How is torque calculated?

Torque is calculated by multiplying the force applied to an object by the distance from the point of rotation at which the force is applied. Mathematically, it can be expressed as T = F x r, where T is torque, F is force, and r is the distance from the point of rotation.

What factors affect torque?

The two main factors that affect torque are the magnitude of the applied force and the distance from the point of rotation at which the force is applied. The angle at which the force is applied can also affect the torque, as well as the properties of the object, such as its mass and shape.

How is torque used in real-world applications?

Torque is used in many real-world applications, including car engines, bicycles, and door hinges. It is also used in physics experiments to measure the rotational motion of objects. In engineering, torque is an important concept in designing machines and structures that need to rotate or have rotational stability.

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