2024/9/13, Hiizu Nakanishi

Sphere Rolling on a Turntable

Simulation speed:
Initial conditions:
position: $a$
velocity: $a\Omega$
direction: deg
Coordinate system:
A sphere rolling without slipping on a turntable traces a circular orbit as viewed from an external (lab) frame. The rotation speed $\Omega'$ depends on the moment of inertia $I$ of the sphere and is given by \[ \Omega' = \frac{1}{1 + Ma^2/I} , \] where $M$ is the mass of the sphere and $a$ is its radius.

For a uniform solid sphere \[ I=\frac{2}{5}Ma^2 \quad\Rightarrow\quad \Omega' = \frac{2}{7}\Omega , \] which means that the sphere completes 2 revolutions while the turntable rotates 7 times.

This simulator allows switching the display coordinate system from the Lab Frame to the Turntable Frame. In the lab frame, the sphere rotates counterclockwise in a circular orbit. However, from the rotating table's viewpoint, the sphere experiences Coriolis force to the right of its direction of motion and moves clockwise.

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