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I am aware of the definition :- $$ \omega_{A/B}=\omega_{A/G}-\omega_{B/G}$$ where /G signifies angular velocity relative to ground or a reference frame at rest.

But I am unable to understand it intuitively I did look on the internet but I did not find anything on why it was defined this way , I have a little trouble with the definition of relative translation velocity as well. I looked for similar question and I did find this but I am simply unable to see why it would be defined that way like how do I get to this definition from ground up using the fact $\omega = \dfrac{d\theta}{dt}$ and understand it intuitively, I do however have a vague understanding like you know A rotated 60 deg and B rotated 30 deg so both of these would have a combined effect leaving the perception for B that A rotated 90 degrees. But I do not really feel it and is not a very clear picture for me at least, any additional resources would also be highly appreciated.

Edit

Someone suggested me this Relative angular velocity and acceleration but I can follow along the math, I am facing problem is in how do you visualise and understand it conceptually and intuitively. Especially even thinking of a roatating rigid rod makes me dizzy.

Mohd Saad
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Think of an example of a rotating object placed on the top of another rotating object (rotating about the same axis.) E.g., a child standing in the center of a roundabout/merry-go-round/carousel. Let us consider there situations:

  • At first carousel doesn't move, but the child rotates about their own axis with angular velocity $\omega_{A/B}$.
  • Now, let carousel rotate with angular velocity $\omega_{B/G}$, while the child doesn't move (in respect to the carousel).
  • Now we combine both movements: the carousel rotates, while the child also rotates, so that their rotation in respect to the ground is even faster.

A more grown-up example could be thinking of an airplane flying along a parallel with angular velocity $\omega_{A/B}=v/R$, where $v$ is its speed in respect to the ground. The Earth itself rotates about its axis, so the overall angular speed of the airplane is the sum of the two.

Roger V.
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