If normal force is the only interaction between particel and torus, there is a minimum velocity to keep the particle always attached to the torus surface.
The coordinate of the particle is

$x=(R+ r\cos\theta) \cos \phi$
$y=(R+ r\cos\theta) \sin \phi$
$z=r \sin\phi$

Due to symmetry, $\frac{d\phi}{dt}=\frac{2 \pi}{T}$ is a constant, and due to gravity $\frac{d^2\theta}{dt^2}=-\frac{g\cos\theta}{r}$

You can adjust mass m (no effect on the motion), both radius R and r with slider.

/htdocs/ntnujava/ejsuser/2/users/ntnu/fkh/particleontorussurface_pkg/particleontorussurface.propertiesFull screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list