For a polyatomic molecule at zero total angular momentum, this paper shows that an internal motion with nonzero internal angular momentum within a (generalized) Eckart frame will produce a net rotation of the (generalized) Eckart frame in the center-of-mass frame. For a polyatomic molecule at nonzero total angular momentum, an internal motion within a generalized Eckart frame with nonzero orbital angular momentum will produce a net rotation of the generalized Eckart frame in the center-of-mass frame. Specifically, at zero total angular momentum, an internal rotation of a diatomic molecule within an atom-diatomic molecule system has nonzero internal rotational angular momentum and produces a counter-rotary net rotation of the orientation of the system (and of its generalized Eckart frame) in the center-of mass frame. Beyond a net overall rotation of an atom-diatomic molecule complex in the center-of-mass frame, a net rotation of the scattering angle of an atom colliding with a rotating diatomic molecule is obtained. A rotation in the recoil angle of an atom departing from a dissociating triatomic molecule has been observed.