  Low-cost coin vibrational motors, used in haptic feedback, exhibit rotational
internal motion inside a rigid case. Because the motor case motion exhibits
rotational symmetry, when placed into a fluid such as glycerin, the motor does
not swim even though its vibrations induce steady streaming in the fluid.
However, a piece of rubber foam stuck to the curved case and giving the motor
neutral buoyancy also breaks the rotational symmetry allowing it to swim. We
measured a 1 cm diameter coin vibrational motor swimming in glycerin at a speed
of a body length in 3 seconds or at 3 mm/s. The swim speed puts the vibrational
motor in a low Reynolds number regime similar to bacterial motility, but
because of the vibration it is not analogous to biological organisms. Rather
the swimming vibrational motor may inspire small inexpensive robotic swimmers
that are robust as they contain no external moving parts. A time dependent
Stokes equation planar sheet model suggests that the swim speed depends on a
steady streaming velocity $V_{stream} \sim Re_s^{1/2} U_0$ where $U_0$ is the
velocity of surface vibrations, and streaming Reynolds number $Re_s =
U_0^2/(\omega \nu)$ for angular vibrational frequency $\omega$ and fluid
kinematic viscosity $\nu$.
