How do I find angular and linear velocity after normal force and "infinite" friction force?

Question

Look at this picture: https://i.sstatic.net/PxZWu.png

Here we have a ball resting on top of a platform (the contact point is marked red). I know the normal vector (marked green). I also know the mass, radius, and current angular and linear velocity of the ball.

Let's say I set the new angular velocity after friction which is always big enough ("infinite") has been applied to: $V_a = V_l \times rN$ where $V_l$ is the linear velocity, $r$ is the radius of the ball and $N$ is the normal vector. Does this math check out, is this correct?

Because this model doesn't work if I leave the ball leaning on the side of the platform where it should obviously roll of the platform and fall. But it doesn't. What is the correct mathematical model for simulating "infinite" friction?

I suppose you will also have this problem when you want to simulate finite friction and the friction doesn't give it's max force.

Answer 1

If C is the center of mass of the ball, and A is the contact point then the velocity of the ball at the contact point is

$$\vec{v}_A = \vec{v}_C + \vec\omega \times (\vec{r}_A-\vec{r}_C) $$

If you have infinite friction then you have no slipping which means $\vec{v}_A =0$. If there was slipping then only the speed in vertical direction should be zero $\hat{n}\cdot\vec{v}_A =0 $, where $\hat{n}$ is the normal direction vector.

I think this is what you are trying to get to with your equation, yet is unclear what you are asking exactly. In your case, the no-slip condition is

$$ \vec{v}_C + \vec{\omega} \times (-\hat{n} r) =0 $$ $$ \vec{v}_C = r \hat{n} \times \vec\omega $$