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I couldn't understand the difference between two different formulations of velocity of a moving particle. In one formulation, we have radial and transverse components of velocity. In the other, we have tangential and normal component of velocity. Why do we need two different formulations? A silly question, aren't the tangential and transverse components of velocity are the same vectors? If we have a circular motion, which formulation is better?

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In the other, we have tangential and normal component of velocity.

That's the correct one.

Forces and curvature

Imagine an object travelling along a line with curvature $R$, then the velocity vector $\vec{v}$ has two components:

  1. $\vec{v_T}$: the tangential component, which runs along the tangent of the trajectory;
  2. $\vec{v_C}$: the normal component which points to the center of the (here imaginary) circle.

Where the trajectory is an actual circle the curvature is replaced by the radius $R$ of the circle.

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  • $\begingroup$ Isn't velocity always tangent to the trajectory? There's no such thing as the normal component of velocity. $\endgroup$ Sep 20 at 7:02

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