Perpendicular force calculated from torque and point of application?

AI Thread Summary
The discussion centers on calculating the perpendicular force (F) that results in a given torque (τ) applied to a body made of mass points in three-dimensional space. The equation τ = r × F is frequently referenced, but the challenge lies in determining F when only τ and the point of application (r) are known. The user expresses skepticism about the impossibility of calculating the unique perpendicular component of F (F⊥) and seeks guidance on deriving it. A proposed method involves calculating an arbitrary force F' using the relationship F' = r × τ / r·r, but the user notes that the resulting torque vector may not be perfectly perpendicular. The conversation highlights the complexities of torque and force relationships in physics.
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I hope I managed to post my question the right place!

I have a body consisting of a bunch of mass-points in ℝ^{3}, and when torque is applied to this body, I'm interested in finding the force that must have caused the torque based on the point of application and the torque vector, which are given.

I see the form;
\tau = r\timesF
quite often, such as it is seen in wikipedia (which offers a nice overview btw).

I understand that it is not possible to calculate F, but I find it hard to believe that F_{\bot} is impossible to calculate since it should be unique, yet I don't see such an equation anywhere. Any pointers would be greatly appreciated!

Cheers,
Miki
 
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Calculate an arbitrary F which satisfies the equation, subtract the component of ##F_{||}##.
 


I see, clever :)

May this arbitrary F (how about we call it F'?) be obtained by;
F' = r×\tau/r\bulletr ?

I'm feeding the result I get back into the form
\tau = r×F
and as I've realized, the \tau and r I am given are not perfectly perpendicular so my \tau' is similar to \tau at best. But that method seems like it would be correct!

Thank you very much!
Miki
 
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