Most people picture the ball sailing away in a straight line away
from the CENTER of the circular path. It's as if there's a force
pulling it away from the center, and that's where the myth of
'Centrifugal force' comes from.
If you shoot a video of the event and view it in slow motion, you
see that after the string breaks, the ball does take off in a straight
line, but the straight line DOESN't come from the center of the spin.
It's a line that's TANGENT to the circle, at the exact point where the
ball was when the string broke. In other words, it's a straight line
in the direction the ball was traveling when the force that was keeping
it on a circle disappeared.
That's exactly what Newton's first law is saying: An object will travel
in a straight line at a constant speed if there's no force to make it
speed up, slow down, or pull it away from the straight line.
The string was doing that, until it let go.
