Retrieving "Curved Path" from the archives

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1. Acceleration

   Linked via "curved path"

   Normal (Centripetal) Acceleration ($\mathbf{a}_n$)
   When an object moves along a curved path, even if its speed remains constant, its direction changes, resulting in acceleration. This component, directed toward the center of curvature, is known as normal or centripetal acceleration. For an object moving in a circle of radius $r$ at a constant speed $v$:
   …

2. Velocity

   Linked via "curved path"

   $$\mathbf{v} = vx \mathbf{i} + vy \mathbf{j} + v_z \mathbf{k}$$
   When analyzing motion in a curved path, velocity is often decomposed into tangential and normal (or centripetal) components relative to the path of motion. The tangential velocity component ($v_t$) describes the rate of change of the object's speed along its trajectory, while the normal component describes the rate at which the direction of motion is changing. The total velocity magnitude is…