- #1

member 392791

I am having difficulty in understanding how the moment about an arbitrary axis is found as the scalar product of the moment about the origin with the unit vector of the arbitrary axis. Can anyone elucidate this?

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- #1

member 392791

I am having difficulty in understanding how the moment about an arbitrary axis is found as the scalar product of the moment about the origin with the unit vector of the arbitrary axis. Can anyone elucidate this?

- #2

Doc Al

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- #3

member 392791

Here are the pages in the textbook that I am referring to, which may help you understand my question more clearly since I am using it as my reference. The second page is in this thread (it appears you can't link the same file in multiple threads)

The topic is figure 3.27 and the confusion is how equation 3.42 is the way it is

EDIT: This is where the 2nd page is linked

https://www.physicsforums.com/showthread.php?t=710626

The topic is figure 3.27 and the confusion is how equation 3.42 is the way it is

EDIT: This is where the 2nd page is linked

https://www.physicsforums.com/showthread.php?t=710626

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- #4

Doc Al

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I see the figure but not the equation. Where again is the second page? (Your link just referred to this thread.)The topic is figure 3.27 and the confusion is how equation 3.42 is the way it is

Edit: I see that you edited your post to link to the second page.

Equation 3.42 just defines the moment along an axis as the

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member 392791

- #6

member 392791

I think I don't understand why its a dot product of lambda. Also, it's strange to me that you can find the moment at a certain point, then pick any point along an arbitrary axis to find the moment around that axis

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- #7

Doc Al

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When you say "entire" axis it sounds like you think that the moment about the axis is somehow greater than the moment about a point. Just the opposite. The moment about an axis is just aWhy is it that I just dot a unit vector with the moment to get the moment around theentireaxis??

Lambda is just a unit vector; taking the dot product with a unit vector is how you get a component of a vector in some direction. Imagine you have a vector ##\vec{F}## in the x-y plane. To get the component of ##\vec{F}## in the x-direction, you'd compute ##\vec{F}\cdot\hat{x} = F \cos\theta##, where ##\theta## is the angle the vector makes with the x-axis. That should be familiar to you.I think I don't understand why its a dot product of lambda.

Yes, you need to convince yourself of this fact. That you can calculate the moment along an axis usingAlso, it's strange to me that you can find the moment at a certain point, then pick any point along an arbitrary axis to find the moment around that axis

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