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Suppose we have a car A moving along a straight path and another car B moving in a circular path. I know from the formula I have studied that the relative velocity of A as observed by B will not simply be

$v_b-v_a$

But I still can not get a 'feel' of why this is so. It just seems so natural to think that the above expression should be the expression for relative velocity in ANY frame regardless of whether it rotates or not, after all, relative velocity is the velocity of one object with respect to other and it seems like a simple difference of velocities should do the trick!

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    $\begingroup$ Taking the difference is fine as long as the velocities are vectors. $\endgroup$
    – Javier
    Commented Apr 10, 2017 at 1:39
  • $\begingroup$ Can you provide an example of what you mean? ie an example in which the simple difference does not work. $\endgroup$ Commented Apr 10, 2017 at 2:50
  • $\begingroup$ @sammygerbil I think the OP is confused about frames. ‘the above expression should be the expression for relative velocity in ANY frame whether it rotates or not'. It would be the same in any inertial frame of reference! $\endgroup$ Commented Apr 10, 2017 at 4:14
  • $\begingroup$ Related to relative velocity in rotating frame of reference and Relative velocity is not the simple difference of individual velocities? posted by the same OP. $\endgroup$ Commented Apr 10, 2017 at 10:26

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I'll give you an idea. Suppose you're sitting on a turntable and your friend is rotating it. Suppose you are at the centre of the turntable. You will see your friend moving right? You are in a rotating frame and both of you are not moving in the ground frame so the difference in the velocities is zero but you still see him moving.


Hope it gives you an intuition.

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  • $\begingroup$ awesome! i finally understand WHY that formula doesn't apply to rotating frames! $\endgroup$ Commented Apr 14, 2017 at 2:08
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Here's a simple example that may help you understand relative velocity involving rotating frame of reference.

Suppose, you and your friend are sitting at diametrically opposite ends of a rotating turntable.

enter image description here

Lets take an instant where your friend's velocity is the vector $v$ wrt an stationary observer sitting just behind the table. Thus, your velocity must be $-v$ in this stationary frame of reference.

By the formula you mention, the relative velocity of your friend wrt your frame of reference then should have been

$v-(-v) = 2v$.

But you will always see your friend at the opposite end of the table stationary, not moving an inch. You see the surrounding is in motion, but not your friend, implying the velocity of your friend relative to you is always 0.

The formula you've mentioned is just a special case of relativity where two people have their velocities always along the same straight line wrt a stationary observer.

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