The angular velocity of a rolling ball is defined as the rate at which the ball rotates about its axis of rotation. As the speed of the ball increases, the ball will also rotate faster about its axis in order to maintain its rolling motion. This is because the faster the ball is moving, the more revolutions it will need to make in order to cover the same distance.
The relationship between the speed of a rolling ball and its angular velocity can be expressed mathematically as follows:
```
v = ωr
```
where:
* v is the speed of the ball in meters per second (m/s)
* ω is the angular velocity of the ball in radians per second (rad/s)
* r is the radius of the ball in meters (m)
As the speed of a rolling ball increases, the radius remains the same. Thus, the only way to increase the speed is to increase the angular velocity. This means that the ball will start rotating faster about its axis as its speed increases.
