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

Look at this picture: http://i.imgur.com/mY8ShkV.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.

• No it is not correct. What are you trying to get out of this pure rolling (no slip) scenario? Dec 11, 2013 at 22:48

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