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Legolaz
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Hello, given the figure above, how do I get the tangential and normal components of a vector in any plane by integration?
You don't, at least not by integration.Legolaz said:
Hello, given the figure above, how do I get the tangential and normal components of a vector in any plane by integration?
SteamKing said:You don't, at least not by integration.
To find the normal vector to a surface, you need to use the gradient:
http://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/grad/grad.html
http://mathworld.wolfram.com/Gradient.html
Legolaz said:Thank you for the reply, Steamking.
Say, I got now the the normal equation for the surface, my tangential would be the 2nd derivative of the gradient function, right?
My next problem is, I want to sum up all Normal and Tangential vectors on the surface, so that I may find the net or resultant vector acting upon the centroid/center of mass of the surface, how to do it?
Legolaz said:]My next problem is, I want to sum up all Normal and Tangential vectors on the surface, so that I may find the net or resultant vector acting upon the centroid/center of mass of the surface, how to do it?
@Legolaz, the image you showed is just a 3-D figure defined by some surfaces. It makes no sense to sum vectors that are perpendicular to each of the bounding surfaces. For a resultant vector, you need to be working with forces, which are not mentioned so far in this thread.SteamKing said:Why? The resultant vector of what?
Yes Mark44, I understood and assume the ones I generally mentioned as "vectors" is referring to Force and Velocity gradients.Mark44 said:@Legolaz, the image you showed is just a 3-D figure defined by some surfaces. It makes no sense to sum vectors that are perpendicular to each of the bounding surfaces. For a resultant vector, you need to be working with forces, which are not mentioned so far in this thread.
The normal component of a vector on a surface is the component that is perpendicular to the surface, while the tangential component is the component that lies parallel to the surface. In other words, the normal component points directly away from the surface and the tangential component lies along the surface.
The normal and tangential components of a vector are related by trigonometric functions. The normal component is equal to the magnitude of the vector multiplied by the cosine of the angle between the vector and the surface, while the tangential component is equal to the magnitude of the vector multiplied by the sine of the angle.
To calculate the normal and tangential components of a vector on a surface, you first need to determine the angle between the vector and the surface. Then, you can use trigonometric functions to find the components as described in the previous answer.
The normal and tangential components are important in physics and engineering because they allow us to analyze and understand the motion of objects on surfaces. The normal component is related to the force perpendicular to the surface, while the tangential component is related to the force parallel to the surface. This information is crucial in designing and predicting the behavior of objects on surfaces.
Yes, the normal and tangential components of a vector can be negative. This indicates the direction of the component, with a negative value indicating the component is in the opposite direction of the positive value. For example, a negative normal component would point towards the surface instead of away from it.