# Spinning Friction

This involves calculating the contact area and then using this to get the torque on the particles as follows:

(1) |

where Fn is the normal force, μ is the coefficient of friction, and R_{disk} is an effective disk radius given by approximating the contact as a disk with area equal to the normal area A_{contact} of the overlap region:

(2) |

The torque acts in the opposite direction to the normal part of the relative angular velocity.

A Limit is applied to this torque to avoid oscillating behavior when the angular velocity is small. This is done by finding the torque which would completely eliminate the angular velocity in one Time Step.

(3) |

The ω_{rel,n} is the normal component of the relative angular velocity, Δt is the Time Step, and I_{x,y,z} is the minimum component of the moment of inertia of either of the 2 contacting objects excluding geometries. The extra C_{safety} factor is to try to avoid possible instability in cases with multiple contacts and at the moment has a value of 0.125.

Also applied is a damping to damp rocking which is defined as:

(4) |

_{n}is the linear damping coefficient in the normal direction from the base model, and ω

_{rel,t}is the tangential part of the relative angular velocity.

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