Tangential Velocity - vs - Tangential Speed

Question

It's the first time for me to ask a question here.

Is there a difference between "Tangential Speed" and "Tangential Velocity"? As far as I know, Speed is scalar quantity defined only with its magnitude while Velocity is a vector defined with both magnitude and direction.

The direction of tangential velocity is always tangent to the circle so that it's always changed while its magnitude is constant (in case of uniform circular motion)

Velocity can be calculated through this relation in the circular path : v = displacement / time

while Speed can be calculated through this relation: v = 2 * pi * radius / time

This shows that the velocity in the circle isn't equal to speed

However, Tangential Velocity Formula is : v = 2 * pi * radius / T

I don't understand how Tangential Velocity is equal to speed although velocity through circle isn't equal to speed!

This really confuses me. Can someone clear this confusion and explain this?

Answer 1

They are typically interchangable. Most people do not speak precisely enough to get them right all the time.

You are correct that in proper usage, speed is a scalar, while velocity is a vector. Thus "tangental speed" should be a scalar describing how fast the object is moving in the tangental direction, and "tangental vector" should be a vector which is in the tangental direction and has a magnitude equal to the tangental speed.

Where you may be getting confused is your velocity formula. V=displacement/time is the formula for average velocity. If you are moving in a straight line, average velocity and velocity align, so you don't have to pay attention to which one you're talking about. In circular motion, however, the direction of the velocity is constantly changing, so average velocity and instantanious velocity do different things. Tangental velocity is a concept related to instantanious velocities, not average ones.

Answer 2

Let me proclaim a comment first (it's too long for a "comment"). As said in this asnswer: https://physics.stackexchange.com/a/285676/157625 Making a word distinction is only a convention for English speakers. In many other languages there is not that distinction, and so you don't have these problems. The "velocity" vs "speed" issue keeps making so much confusion, and it is only because you insist giving $|\vec{v}|$ a different name. However, you can talk about a force and it can be $F$ or $\vec{F}$, so of course we are a little reluctant of taking the word "speed".

The rest of the world uses the same word an nothing happens, provided that you have the concept clear. You have to know what you're talking about. Or you can just say "velocity module" and "velocity vector", if you want to highlight that.

Now, going to your question, both formulas are the same. The thing is that you have to substitute "time" but $T$. You say that velocity (or speed) is "displacement/time", yes but it means "displacement / (time elapsed during that displacement". If you say

$v= \frac{ 2\pi r}{time}$, you have to use the time required for that distance, which is the full loop, and the time required to complete a full turn is called period, $T$.

Answer 3

Tangential velocity and tangential speed are not the same. What you are referring to, is the magnitude of the tangential velocity, loosely referred to, simply, as velocity. Technically, the terminology is wrong, and strictly speaking, tangential velocity comes with the a direction, $\hat{\theta}$, while speed is it's magnitude.