Calculate the torque on a rigid body

In summary, it is not possible to calculate the torque on a rigid body without specifying the origin. This is because the torque vector is oriented in 3D-Euclidean space and the point of orientation is relative to the origin in a chosen coordinate system. If the coordinate system is removed, the direction and magnitude of the torque would have to be assumed instead of calculated. Therefore, the torque cannot be computed without an origin specified, as it would cease to exist as a vector. This concept can be further understood by considering manifold-to-manifold transformations and using spherical coordinates.
  • #1
DNA
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Can someone please tell me if it is possible to calculate the torque on a rigid body without specifying the origin?
 
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  • #2
DNA said:
Can someone please tell me if it is possible to calculate the torque on a rigid body without specifying the origin?
:smile: if you think about it a torque vector is oriented in the 3D-Euclidian space. the point of orientation is relative to some orgin in a chosen coordinate system. Now if you take the coordinate system away then you just have the vector part of the torque. this would imply that the direction and magnitude of the torque would be assumed and not computed, because the torque equation doesn't allow it to calculated without the origin specified(i.e. transformations from manifold-to-maniflold can occur). therefore, the torque cannot be computed without an origin, because it would cease to exist as a torque vector.this might not seem so obvious, but try the following problem and take away the origin from your coordinate system and try the same problem with the origin in the coordinate system(hint: use spherical coordinates). think about the torgue developed by the rotation of the Earth go through the calculation. keeping what I previously said in mind one should realize the validity of this rationalization. :smile:
 
  • #3
I think that i understand, manifold to manifold transformations,spherical coordinates! I am only beginning my physics journey, it would seem that i have a long way to go.
 

1. What is torque?

Torque is a measure of the force that can cause an object to rotate around an axis. It is commonly referred to as a twisting or turning force.

2. How is torque calculated?

Torque is calculated by multiplying the applied force by the distance from the axis of rotation to the point of force application. The formula for torque is T = F * r, where T is torque, F is the applied force, and r is the distance from the axis of rotation.

3. What is a rigid body?

A rigid body is an object that does not deform or change shape when forces are applied. It maintains a constant shape and size, and all points on the body move in a parallel manner when a force is applied.

4. How do you calculate the torque on a rigid body?

To calculate the torque on a rigid body, you need to know the applied force and the distance from the axis of rotation. Once you have these two values, you can use the formula T = F * r to calculate the torque.

5. What are some real-life applications of calculating torque on a rigid body?

Calculating torque on a rigid body is important in fields such as engineering, physics, and mechanics. It is used in designing machines and structures, understanding how forces affect objects, and determining the efficiency of different mechanical systems.

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