# Is there any video I can use to visualise why velocities change in moving rotating reference frames?

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!

• Taking the difference is fine as long as the velocities are vectors. – Javier Apr 10 '17 at 1:39
• Can you provide an example of what you mean? ie an example in which the simple difference does not work. – sammy gerbil Apr 10 '17 at 2:50
• @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! – Kunal Pawar Apr 10 '17 at 4:14
• @Javier The velocities are always vectors. Don't be so glib, you are in a stackexchange site! – Deechit Poudel Apr 10 '17 at 8:31
• 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. – sammy gerbil Apr 10 '17 at 10:26

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.

• awesome! i finally understand WHY that formula doesn't apply to rotating frames! – Sakazuki Akainu Apr 14 '17 at 2:08

I too had some difficulty grasping it. However, I figured out a way I could convince myself. Suppose, you and your friend are sitting at the opposite ends of any diameter of a rotating turntable.

At any instant, your friend's velocity is $v$. Thus, your linear velocity must be $-v$. And by the formula you mention, the relative velocity of your friend must be

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

But you will always see your friend at the opposite end of the turn table, $STATIONARY$ not moving an inch (relative to you).

In fact, the formula you've mentioned is just a special case of classical relativity where two people have their velocities always along the same straight line.