Imagine that the ball is rolling with no slipping. When it rotates by 1 radian then it will move a vertical distance equal to the radius of the ball (see definition of radian)

So:

v = r * w

where:

- v = linear velocity
- r = radius of ball
- w = angular velocity

So the angular velocity is directly linked to linear velocity. Can we work directly from the linear velocity in our program, calculating angular velocity from linear velocity when required?

Of course, this assumes that there is no slipping. For that to be true the linear momentum must be exactly matched to the rotational momentum.

### Direction

If there is no slipping then the direction of travel is related to the axis of rotation. For instance, if the ball is rotating about the y axis, then it will be travelling in the x direction.