Two solid bodies rotate about stationary mutually perpendicular intersecting axes with constant angular velocities `omega_1=3.0rad//s` and `omega_2=4.0rad//s`. Find the angular velocity and angular acceleration of one body relative to the other.

Explanation

The angular velocity is a vector as infinitesimal rotation commute. Then the relative angular velocity of the body 1 with respect to the body 2 is clearly.
`vecomega_(12)=vecomega_(1)-vecomega_2`
as for relative linear velocity. The relative acceleration of 1 w.r.t. 2 is
`((dvecomega_1)/(dt))_(s')`
where S' is a frame corotating with the second body and S is a space fixed frame with origin coinciding with the point of intersection of the two axes,
but `((dvecomega_1)/(dt))_s=((dvecomega_1)/(dt))_s+vecomega_2xxvecomega_1`
Since S' rotates with angular with angular velocity `vecw_2`. However `((dvecomega_1)/(dt))_S=0` as the first body rotates with constant angular velocity in space, thus
`vecbeta_(12)=vecomega_1xxvecomega_2`.
Note that for any vector `vecb`, the relation in space forced frame `(k)` and a frame `(k^')` rotating with angular velocity `vecomega` is
`(dvecb)/(dt):|:_K=(dvecb)/(dt):|_K+vecomegaxxvecb`