What is the Initial Torque of a Rod with an Acting Force?

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Homework Help Overview

The problem involves calculating the initial torque of a rod subjected to a force acting at its upper end. The rod is oriented along the y-axis and has a specified length, with the force expressed in vector form.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of torque and its calculation using the cross product. There are inquiries about how to apply this definition to the specific choices provided in the problem.

Discussion Status

Some participants have provided hints regarding the definition of torque and suggested finding the expression for the position vector. The discussion is ongoing, with no clear consensus on the correct answer yet.

Contextual Notes

Participants are working within the constraints of the problem statement and the multiple-choice format, which may limit the exploration of potential solutions.

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Homework Statement



A rod is initially along the y-axis and has
length ℓ. A force F =ˆı F1 +ˆj F2 + ˆk F3
acts at the upper end of the rod.
What is the initial torque ~τ about the lower
end of the rod?
1. Zero
2. ˆıF3 ℓ
3. −(ˆı F3 +ˆj F2 + ˆk F1) ℓ
4. (ˆıF3 − ˆk F1) ℓ
5. (ˆıF1 +ˆj F2 +ˆk F3) ℓ


Homework Equations





The Attempt at a Solution

 
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Hint: What's the definition of torque in terms of a cross product?
 


Doc Al said:
Hint: What's the definition of torque in terms of a cross product?

I am not sure. Please help
 


\vec{\tau} = \vec{r} \times \vec{F}
 


What answer would that be with respect to my choices?
 


shiby4444 said:
What answer would that be with respect to my choices?
That's for you to figure out! All I did was give a definition of torque. Hint: Find an expression for \vec{r} (its magnitude is ℓ) and perform the cross product.
 

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