Why doesn't a stone fly off when twirled in a circle on a string?

A stone doesn't fly off when twirled in a circle on a string due to the centripetal force acting on it.

When a stone is twirled in a circle on a string, it is constantly changing direction, which means it is accelerating. This acceleration is towards the centre of the circle and is caused by a force known as the centripetal force. The centripetal force is provided by the tension in the string, which pulls the stone towards the centre of the circle, preventing it from flying off.

The stone, due to its inertia, tends to move in a straight line. However, the string prevents this from happening. The tension in the string acts as a centripetal force, pulling the stone towards the centre of the circle. This force is always perpendicular to the velocity of the stone and is responsible for the change in direction of the stone, which is an acceleration. According to Newton's second law of motion, an acceleration is caused by a force. In this case, the force is the tension in the string.

The magnitude of the centripetal force is given by the equation F = mv^2/r, where m is the mass of the stone, v is the velocity of the stone and r is the radius of the circle. This equation shows that the centripetal force increases with the square of the velocity and decreases with the radius. Therefore, if the stone is twirled faster or the string is shortened, the tension in the string must increase to provide the necessary centripetal force.

In conclusion, the stone doesn't fly off when twirled in a circle on a string because the tension in the string provides the necessary centripetal force to keep the stone moving in a circle. This is a direct application of Newton's second law of motion, which states that an acceleration is caused by a force.