Help interpreting the physics of a rolling ball

Question

I'm using this article for reference. I understand handling the collision aspect, but I can't figure out how to calculate the new velocity once the ball collides with the ramp. Without it the ball just slides down the slope and stops at the bottom, with no horizontal velocity generated from the descent.

The equation mentioned is

tangentialVelocity = velocity – (velocity * normal)normal

Which I've tried as

        ball.velocityX = _magnitude - (_magnitude * _normalX) * _normalX;
        ball.velocityY = _magnitude - (_magnitude * _normalY) * _normalY;

to no avail.

Here is what I've done so far, which finds how far the ball is intersecting in the ramp and moves it outside.

        var _distance:int = FP.distance(circleWorld.x, circleWorld.y, ball.x, ball.y);
        var _penetration:int = _distance + ball.radius - worldRadius;

        if (_penetration > 0)
        {
            var _componentX:int = circleWorld.x - ball.x;
            var _componentY:int = circleWorld.y - ball.y;

            var _normalX:Number = _componentX / _distance;
            var _normalY:Number = _componentY / _distance;

            ball.x += _normalX * _penetration;
            ball.y += _normalY * _penetration;
        }

Answer 1

It doesn't look like your code is actually tracking the ball's rotation. The rotational inertia of the ball will have a very great effect on how quickly it descends the ramp, and how long it'll keep moving after it exits the ramp.

Some ideas for further thought here: http://physics.bu.edu/~duffy/sc527_notes06/race.html

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Edited to clarify: Your current simulation is modeling the ball sliding down a frictionless ramp. A real ball on a real ramp will likely not move at all without turning. You can calculate the forces on the ball using equations like those in the web page I linked to above. Once you know the torque on the ball, you can calculate how quickly it turns.

It'll roll down the ramp at approximately the same speed that it's rotating at, which is to say the distance travelled along the ramp in a given time will approximately equal the arc length that the perimeter rotates in the same time (some slippage will occur in a realistic situation).

Answer 2

tangentialVelocity = velocity – (velocity * normal)normal

That is vector maths, the * in this case means dot product, both velocity and normal are vectors.

A dot product is calculated like so:

dotp = vector1.x * vector2.x + vector1.y * vector2.y

So your code should as best I can tell be this:

dotp = ball.velocityX * _normalX + ball.velocityY * _normalY
ball.velocityX -= dotp * _normalX;
ball.velocityY -= dotp * _normalY;

And for the sake of completeness _normal must of course be length 1 and pointing in the correct direction for this to work.