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I watched a video on khan academy(https://www.khanacademy.org/science/physics/centripetal-force-and-gravitation/centripetal-acceleration-tutoria/v/visual-understanding-of-centripetal-acceleration-formula) it said (around 3:29) that the radius of a circle is equal to the magnitude of the velocity. I am not exactly sure how the instructor concluded this?

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  • $\begingroup$ Please provide an exact quote. It seems more likely that the professor said the velocity is proportional to the radius. $\endgroup$
    – S. McGrew
    Oct 10, 2020 at 18:13
  • $\begingroup$ Here is the quote: "And we already know the magnitude of the velocity vectors is this quantity v(the speed), this scalar quantity. So the radius of this circle is v(the speed)" $\endgroup$ Oct 10, 2020 at 18:24
  • $\begingroup$ Two physical quantities can’t be equal if they have different units. For example 3 meters (a possible radius) and 3 meters per second (a possible speed) cannot be compared. $\endgroup$
    – G. Smith
    Oct 10, 2020 at 18:49
  • $\begingroup$ @G.Smith if that is so why does the instructor say that the magnitude of velocity is equal to the radius? $\endgroup$ Oct 10, 2020 at 18:51
  • $\begingroup$ Some possibilities are that you misheard, you misunderstood, the instructor doesn’t know what they’re talking about, the instructor has a very unconventional and confusing way of talking about this, the instructor simply misspoke, etc. (I have not watched the video.) $\endgroup$
    – G. Smith
    Oct 10, 2020 at 18:53

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You misunderstood, he is just saying that the velocity vectors also form a circle that has a constant radius in velocity space. Not that it is the radius of the trajectory.

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