What variables are needed to find a moment?

[Alex Katko]

Homework Statement

You wish to find the moment at the origin produced by a force, ̅F= {Fi}̂, that is applied at r= {̂ai+bj +ck ̂}. Which variables (F,a ,b,c , ) do we need to know to find a numerical answer? Explain using math and figures.

Homework Equations

Mo = r x F

The Attempt at a Solution

I know that the above equation is used to find a moment. Therefore, to me it makes sense that all variables (a,b,c,F) are needed unless you were given some sort of extra information (coordinate direction angles). Needing all the variables seems to be too simple. Any advice or hints are appreciated!

 

[haruspex]

Homework Statement

You wish to find the moment at the origin produced by a force, ̅F= {Fi}̂, that is applied at r= {̂ai+bj +ck ̂}. Which variables (F,a ,b,c , ) do we need to know to find a numerical answer? Explain using math and figures.

Homework Equations

Mo = r x F

The Attempt at a Solution

I know that the above equation is used to find a moment. Therefore, to me it makes sense that all variables (a,b,c,F) are needed unless you were given some sort of extra information (coordinate direction angles). Needing all the variables seems to be too simple. Any advice or hints are appreciated!

Perform the cross product algebra and see what happens.

 

[Alex Katko]

Perform the cross product algebra and see what happens.

Performing the cross product gives me: (bFz-cFy)i + (cFx - aFz)j + (aFy - bFx)k. All variables (the 3 components of F and a,b,c show up).

 

[haruspex]

Performing the cross product gives me: (bFz-cFy)i + (cFx - aFz)j + (aFy - bFx)k. All variables (the 3 components of F and a,b,c show up).

You are given $\vec F=F\hat i$. So what are Fx, Fy and Fz?

 

[Alex Katko]

You are given $\vec F=F\hat i$. So what are Fx, Fy and Fz?

Ohh i think i am understanding. Fx = Fi. Fy = 0 Fz = 0

 

[haruspex]

Ohh i think i am understanding. Fx = Fi. Fy = 0 Fz = 0

Almost. Fx=F, a scalar. There is no variable Fi.

 

[Alex Katko]

Almost. Fx=F, a scalar. There is no variable Fi.

If Fy and Fz are both zero, then the croos product becomes cFxi - bFxj. Therefore, the variables needed are F,c, and b

 

[haruspex]

If Fy and Fz are both zero, then the croos product becomes cFxi - bFxj. Therefore, the variables needed are F,c, and b

Yes.