Plane Curvilinear Motion - n-t Coordinates

 

Normal - Tangential coordinate system

 

Watch the animation and consider how easy or hard it would be to solve for the acceleration of the pink car.

 

 

It would be fairly difficult to solve for the acceleration of a car using the x-y coordinate system. The rectangular coordinate system is much better for solving straight line motion or motion where the acceleration in the x and y-directions are independent. The n-t coordinate system is more natural for curved paths that are known.

 

The n-t coordinate system is used when the path of the particle is known. It is a body fixed coordinate frame that is attached to and moves with the particle.

• t-axis: The positive t–axis is in the direction of motion, tangent to the path curve.
• n–axis: The positive n–axis is perpendicular to the t–axis and is directed toward the center of curvature.

 

 

Step through the following animation to see how the n-t coordinate axes are attached to the body.