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I have a car moving in straight line with certain time-varying acceleration and there is another car moving in a curvilinear way along some curved path with some time-varying acceleration. The inertial reference frame is say fixed at some point in space. The relative velocity and acceleration at any instant is calculated.

Why is the relative velocity of the car moving in curved path from the point of view of the car moving in straightline, different from the relative velocity of the car moving in straightline from the point of view of the car moving in the curved path? I know that in mathematical formulation this will involve the instantaneous angular velocity of the car following the curved path. But that is not very intuitive to me. Is there any way I can understand this situation clearly and more intuitively,i.e., Visualize it.

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  • $\begingroup$ This belongs in Physics.SE, where you will find a few dozen duplicates of this question. $\endgroup$ – Carl Witthoft Jan 6 '16 at 12:54
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Get a friend, and stand 15 feet (5m) from your friend. Your friend holds out their arm and points at you, then you do the same.

Now, you try turning in a circle. Your friend's shoulder doesn't move because your relative linear velocity is zero.

Your shoulder has to move to keep pointing at your friend, though, because from your point of view, your friend is running circles around you. Your friend does have a relative linear velocity, and so you have to constantly adjust to keep pointing at them.

This is the same reason why it looks like the sun translates across the sky. The sun is (relatively) stationary, but the Earth rotates. Since you are on the Earth, your point of view is that the Earth is stationary and the sun is translating - this is why the original view was that the Earth was the center of the solar system.

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