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A slight confusion on terminology.

Tangential speed refers to the linear speed when travelling across a circular path, it refers to the distance covered across the circular path for a given time. I have seen the word Tangential velocity used with tangential speed in various websites, shouldn't tangential velocity refer to displacement with time in that motion?

Is there something wrong in my point? Tks for helping

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5 Answers 5

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In a 2D radial coordinate system, there are two orthogonal directions: radial and tangential. You could call these $\hat{r}$ and $\hat{\theta}$. Tangential velocity is the component of velocity in $\hat{\theta}$. It is still directional because it can be positive or negative. Tangential speed is the magnitude of this velocity.

Although the magnitude of the velocity vector has a special name (speed), it's still okay to talk about velocity components or velocity magnitude and call it velocity. Most vectors don't have a special name for their magnitude, anyway. For example, the magnetic field vector and the magnetic field strength are $\vec{B}$ and $B$ and they could both be referred to as just magnetic field (the surrounding context should make it as clear as it needs to be whether magnitude or vector is meant).

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Tangential velocity

If an object travels from point $A$ to point $B$ (see above schematic) along the black line, the red arrows represent the tangential velocity vectors $\vec{v}$ at various points along the trajectory.

The velocity vector $\vec{v}$ has both a direction and a magnitude (or scalar) $v$ (represented by the length of the arrow).

The concept is not restricted to uniform circular motion but applies to all non-linear motion. In that case the direction of the tangential velocity vector will constantly change (the scalar may be constant or vary in time, depending on the case).

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The term "Tangential speed" is the most suitable way to use since the velocity is not uniform for a circular motion since the direction of the velocity is changing through out the pathway.

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Speed is usually meant to be a scalar referring to the norm of the velocity vector. When people talk about tangential velocity, I believe they are referring to the magnitude of the tangential component of the velocity (i.e. a scalar number) in a curved motion at a given time (or maybe a constant value over the circular path). In that sense, tangential velocity and tangential speed are the same thing. I think this is technically not correct, but it is definitely used a lot.

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  • $\begingroup$ It is perfectly acceptable to refer to one component of a vector using the overall name of the vector: radial velocity, radial magnetic field, X velocity, Y velocity, etc. Not every quantity has a special name for its magnitude the way velocity has speed. Furthermore, vector components can be negative, and magnitudes such as speed are positive definite. $\endgroup$
    – EL_DON
    Oct 6, 2016 at 16:55
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Term tangential is used to refer instantaneous in circular motion. Tangential speed is instantaneous speed during circular motion and tangential velocity is the instantaneous velocity having direction along direction.

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