Working on 3d forces in space. In my textbook it list the force components as: F
ID: 1821113 • Letter: W
Question
Working on 3d forces in space. In my textbook it list the force components as:Fsubx=Fsin?ycos?f Fsuby=cos?y Fsubz=Fsin?ysinf Working some problems they change up the sin and cos and I dont understand why. I know that depending on which way the force is some components will be negative but cant figure out why in the problem I am working now the sin and cos are switched for Fx and Fz is both cos. My problem is not on cramster or anywhere else on the web, just looking for an explanation.
Fsubx=Fsin?ycos?f Fsuby=cos?y Fsubz=Fsin?ysinf Working some problems they change up the sin and cos and I dont understand why. I know that depending on which way the force is some components will be negative but cant figure out why in the problem I am working now the sin and cos are switched for Fx and Fz is both cos. My problem is not on cramster or anywhere else on the web, just looking for an explanation.
Explanation / Answer
seems to mea mis-represented form of conversion from spherical coordinates to cubic coordinates. In vector calculus there are at least three ways to represent a point (or a vector) in 3-space, R-3, or 3-dimensional space. One is "cubic" (x,y,z), one is cylindrical (r,theta,z), and one is spherical (rho, theta, phi) where rho is the magnitude of the vector to point P (x^2+y^2+z^2). Theta is the angular displacement between the positive x-axis and the projection of the vector to point P on the xy-plane, and phi is the angular displacement between the positive z-axis and the vector to point P. in any event, let the force be the vector in question the x component is rho * sin(phi) * cos(theta) the y component is rho * sin(phi) * sin(theta) the z component is rho * cos(phi) however if they are saying the vector is some angle off the xy-plane you must then use the compliment to phi (pi/2-phi) I choose alpha as a name. then sin(phi)=cos(alpha) and cos(phi)=sin(alpha) then it looks like this... the x component is rho * cos(alpha) * cos(theta) the y component is rho * cos(alpha) * sin(theta) the z component is rho * sin(alpha) then, to make things confusing, if they choose to "swing" the axis around ... a new set of conversions must be created. wikipedia has a diagram that will help in the heading "spherical" coordinates. ultimately it depends on the words of the problem, a knowledge of physics, and the ability to properly manipulate mathematics to fit the context. There are conventions, but they are not always adhered to precisely and it its up to you to translate the words into sensible notation for a solution.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.