What is the relationship between the torque and position vectors?

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Homework Help Overview

The discussion revolves around the relationship between torque and position vectors in a physics context, specifically focusing on a scenario involving a 5.0 kg object with given position and acceleration vectors. Participants explore the calculation of torque and its properties.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of torque using the cross product of the position and force vectors. There is an examination of the perpendicularity of the torque and position vectors, with some questioning the correctness of the calculations and interpretations presented.

Discussion Status

Some participants have provided calculations and expressed differing views on the results, particularly regarding the sign and magnitude of the torque. There is an acknowledgment of the relationship between the torque and position vectors, with references to the dot product indicating perpendicularity. However, no consensus has been reached on the interpretations or correctness of the calculations.

Contextual Notes

One participant mentions being marked wrong on an exam for similar calculations, suggesting that there may be specific expectations or conventions in the problem setup that are under discussion.

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A 5.0 kg object at r= i^+2j^+3k^ meters has an acceleration a=5i^+6j^-7k^ m/s^2

a)what is the objects torque around the origin of the cordinate system
b)prove that the torque is perpendicular to the position vector r

a)
t^=rXma=-10<16,-11,2>
t=-10(381)^1/2

b)
<1,2,3>*<16,-11,2>=0
 
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Do you have a question? What you have looks fine to me.
 
I was marked wrong for that on an exam
 
The torque T is a vector, and I get what you get.

The magnitude of the torque (which wasn't asked for), |T| is +10*sqrt(381), not -10sqrt(381) as you had.

The dot product of <1, 2, 3> and 10<-16, 11, -2> is 0, so the two vectors are perpendicular. Maybe you were supposed to prove that the torque and position vectors are perpendicular in general, not just for the values in this problem.
 

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