  We elucidate the dynamics of a thin spherical material shell with a
tangential pressure, using a new approach. This is both simpler than the
traditional method of extrinsic curvature junction conditions (which we also
employ), and suggests an expression for a `gravitational potential energy' of
the shell. Such a shell, if slowly spinning, can rotationally drag the inertial
frames within it through a finite angle as it collapses and rebounds from a
minimum radius. Rebounding `spherical' and cylindrical pulses of rotating
gravitational waves were studied previously. Here we calculate their angular
momentum and show that their rotational frame dragging is in agreement with
that of the rotating spherical shell and a rotating cylindrical dust shell.
This shows that Machian effects occur equally for material and analogous
`immaterial' sources.
