Find Torque About Any Line: How to Calculate n Vector

[Vertol]

I know how to find a torque at anyone point, and about the x,y, and z axis.

General equation is t = n dot (r X F)

where t is the torque, n is unit vector

I know that to find torque about any axis, suppose the y-axis then n=(0,1,0) However, I don't know how to find n of any line.
I am working on a practice problem for a test where the line is x/2 = y/1 = z/-2

Any help would be appreciated.

 

[willem2]

find 2 points on the line, use the position vector of point2 - point1.

If this vector has length 1 you're done. If not, multiply the vector by
some constant to make the length equal to 1.

 

[astrokreng]

To find the torque about any line, you can follow these steps:

1. Determine the unit vector (n) that is perpendicular to the line of interest. This can be done by taking the cross product of two vectors that lie on the line. For example, in the given line x/2 = y/1 = z/-2, we can choose two points on the line, such as (2,1,-4) and (1,1,-2). Taking the cross product of these two points will give us the unit vector n = (2,-6,3).

2. Once you have the unit vector, you can use the general equation for torque (t = n dot (r X F)) to calculate the torque about the line. Here, r is the position vector from the point of rotation to the point of application of force, and F is the force vector. Make sure to choose the correct values for r and F based on the given problem.

3. Plug in the values in the equation and solve for torque. Remember to use the magnitude of the force vector, as torque is a scalar quantity.

In summary, to find the torque about any line, you need to determine the unit vector perpendicular to the line and then use the general equation for torque to calculate the value. I hope this helps you with your practice problem and understanding of torque calculations. Good luck on your test!