Title: Motion of a rod pushed at one point in a weightless environment in space,
Abstract: We analyze the motion of a rod floating in a weightless environment in space
when a force is applied at some point on the rod in a direction perpendicular
to its length. If the force applied is at the centre of mass, then the rod gets
a linear motion perpendicular to its length. However, if the same force is
applied at a point other than the centre of mass, say, near one end of the rod,
thereby giving rise to a torque, then there will also be a rotation of the rod
about its centre of mass, in addition to the motion of the centre of mass
itself. If the force applied is for a very short duration, but imparting
nevertheless a finite impulse, like in a sudden (quick) hit at one end of the
rod, then the centre of mass will move with a constant linear speed and
superimposed on it will be a rotation of the rod with constant angular speed
about the centre of mass. However, if force is applied continuously, say by
strapping a tiny rocket at one end of the rod, then the rod will spin faster
and faster about the centre of mass, with angular speed increasing linearly
with time. As the direction of the applied force, as seen by an external
(inertial) observer, will be changing continuously with the rotation of the
rod, the acceleration of the centre of mass would also be not in one fixed
direction. However, it turns out that the locus of the velocity vector of the
centre of mass will describe a Cornu spiral, with the velocity vector reaching
a final constant value with time. The mean motion of the centre of mass will be
in a straight line, with superposed initial oscillations that soon die down.