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I've read in Hibbeler Dynamics, page 131, that when considering a coordinate system with normal and tangential axes, the sum of binormal forces equals zero. I don't understand why this is true, maybe I'm a little foolish right now. I'd be appreciated if someone could explain it.

Note: Binormal force -> A force that is orthogonal to the two axes, the normal and tangential axes.

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The normal and the tangential axis at any moment describe a trajectory in a plane, (even in the generic 3d motion). I.e. if you sum all the forces and obtain a resultant force acting on the particle, then the projection of the resultant force:

  • on the tangential axis will be responsible for the increase/decrease of the velocity magnitude.
  • on the normal axis will be responsible for the change in direction. Or more precisely, what is left from the resultant force (after you remove the tangential component) will be on a plane. The tangential and the normal axis define that plane.

The normal axis might rotate in space (in essence it describes a Instantaneous Center at each moment).

On the binormal axis then (by definition of the tangential and the normal system) the component will be zero.

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