A ball whirls on a string, counterclockwise as drawn from above. Then the string snaps. Most people picture the ball shooting straight outward, away from the center, as if the circling had wound up an outward force. Watch what actually happens: the ball leaves along a straight line that just touches the circle.
Why that line?
At the instant the string snaps, the ball has a velocity, and in uniform circular motion that velocity points along the tangent at the ball's position. The snap changes none of that. It only removes the one inward force.
Before the snap, the string's tension turned the ball's path into a circle at every instant. After the snap, no force points at the center.
So the path after the snap is the straight line along the tangent at the snap point, at the speed the ball already had.
Not a straight line outward from the center: the ball never had a velocity pointing outward, and no outward force ever acted to give it one.
Not a widening spiral either: a spiral is a curving path, and a curving path needs a net force. After the snap there is none in the horizontal plane.
To predict the direction, you need two facts: the ball's position on the circle, and its sense of travel, clockwise or counterclockwise as drawn on the page. The tangent line at the point is at a right angle to the line joining the point to the center, and the sense of travel picks which way along the tangent the ball goes.
A sling whirls a stone in a horizontal circle, and the slinger releases the cord. What path does the stone take at the instant of release?
An athlete whirls a hammer in a circle and releases its wire. In which direction does the hammer move at the instant of release?
At release, the hammer's velocity points along the tangent at its position on the circle.
The release removes the inward force: because without a net inward force nothing pulls the object toward the center, and it keeps moving in a straight line along the tangent (Newton's first law).
The hammer moves along the straight tangent line at its release point, in its direction of travel at that instant.
A ball rolls around the inside of a circular hoop lying on a gym floor and escapes through a gap in the hoop. Why does the ball leave along the tangent line?
Seen from above, a rubber stopper whirls counterclockwise on a cord and is at the northernmost point of its circle when the cord is cut. Which way does the stopper first head?
The tangent at the northernmost point is at a right angle to the north-pointing line from the center: it runs east-west.
The stopper travels counterclockwise as drawn, so at the northernmost point its velocity points west.
The cut removes the inward force, and the stopper keeps that westward velocity.
The stopper heads due west, along the tangent.
An eraser whirls on a string over a smooth table, and the string snaps. Pavel says: 'The eraser now slides in a straight line, at the speed it had when the string snapped.' Is he correct?
Seen from above, a fishing weight whirls clockwise on a line and is at the northernmost point of its circle when the line snaps. Which way does the weight first head?
Seen from above, a bolt whirls counterclockwise on a cord and is at the easternmost point of its circle when the cord snaps. Which way does the bolt first head?
A stopwatch whirls on its strap, and the strap snaps. Which statement about the stopwatch's motion just after the snap is correct?