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Well, tangential velocity is the velocity the object would have it were to leave the circular motion, and start moving in a straight line. So, an example I looked up really quickly is.......
" Imagine you're on a merry-go-round, your tangential speed is the speed at which you are moving around in a circle.
If you were to walk closer to the center, your tangential speed would increase, and if you were to walk further out it would decrease, even though the speed at which the merry-go-round rotates remains the same.
You can also think about it in terms of centripetal acceleration.
a=v^2 / r
The v that you use for that equation for velocity would be the tangential speed/velocity."