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enter image description hereI want someone to kindly check whether I am doing (understanding) the math correctly or not.

So, let's consider two bodies with constant angular velocities $\omega_1 \hat y$ and y $\omega_2 \hat x$ so the relative angular velocity of body 2 with respect to 1 is, $\vec \omega=\omega_2 \hat x -\omega_1 \hat y$

Now, the understanding (checking) part begins.

Let's calculate the relative angular velocity of body 2 w.r.t 1,

So now I'm going to consider the $\hat x$ unit vector rotating about the $\hat y$ vector. ( $\hat y$ vector remains stationary ) Thus when taking the time derivative of $\vec \omega$, the $\omega_1 \hat y$ term vanishes (constant) but the derivative of $\omega_2 \hat x$ is $\omega_2\dot{\hat x}$.

The $\dot{\hat x}$ has its direction towards the negative $z-axis$ and it's value is $\omega_1$ so, $$\dot{\hat x}=-\omega_1 \hat z$$

giving us, $$\dot {\vec \omega}=-\omega_1 \omega_2 \hat z$$

Am I right ?

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So, let's consider two bodies with constant angular velocities ω1y and ω2x so the relative angular velocity of body 2 with respect to 1 is, ω⃗ =ω2x^+ω1y^

i think we are making an error here

The angular velocity of body 2 with respect to body 1 will look like = angular velocity of body 2- angular velocity of body 1

and if you go for calculating angular acceleration of body 2 w.r.t. body 1 it will be cross product of the two angular velocities.

Pl see:Relative angular velocity and acceleration though this could be a comment only.

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  • $\begingroup$ yes yes sorry. i was thinking about a minus sign and wrote a plus instead. my bad. I'll correct it now. thank you. $\endgroup$ – Subhranil Sinha Mar 20 '16 at 7:46
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    $\begingroup$ thanks for editing;it appears that the direction of angular acceleration is correct. $\endgroup$ – drvrm Mar 20 '16 at 8:35

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