2024/5/30, Hiizu Nakanishi

Rolling Coin, Ring, and Hollow Cylinder

Shape Parameters: Inner/Outer radius =
Thickness/Outer radius =
Friction Coefficient: $k=$
Inclination Angle
$\theta=$ 0 deg
$\phi=$ 0 deg
Angular Velocity
$\omega_Z=$ 0
$\omega_Y=$ 0
$\omega_X=$ 0
This simulation extends the rolling coin simulation to rings and thick-walled hollow cylinders. You can change the size and thickness by the shape parameters sliders.

Dissipation is modeled as a decay in angular velocity, similar to the coin case.

At the contact point with the floor, you can toggle between "No Slip" and "Slip" conditions. In the slip case, the friction coefficient $k$ gives a resistive force $\vec F$ against the slip velocity $\vec v_{\rm slip}$ as \[ \vec F = -k\, \vec v_{\rm slip}. \]

In the "No Slip" case, $\vec v_{\rm slip}=0$ and $k \to \infty$. A large $k$ in the slip condition approximates no slip.

The parameter values use normalized units: radius $a$, mass $M$, and gravitational acceleration $g$ are all set to 1, i.e., $a=M=g=1$.

For detailed equations, refer to the calculation notes.
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